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Explanations and examples of hypothesis testing and confidence intervals, including the null and alternative hypotheses, forms of hypothesis tests, and the calculation of p-values and confidence intervals. It also covers left-tailed, right-tailed, and two-tailed tests, as well as the interpretation of results.

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2023/2024

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Download Hypothesis Testing and Confidence Intervals and more Exams Health Physics in PDF only on Docsity! MATH 225N Week 8 Final Exam -Version 1 & 2 -with 100% verified solutions-2023-2024 MATH 225N Week 8 Final Exam Question 1 1/1 points A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. That is correct! H0: μ≠33; Ha: μ=33 H0: μ=33; Ha: μ≠33 H0: μ≥33; Ha: μ<33 H0: μ≤33; Ha: μ>33 Answer Explanation Correct answer: H0: μ=33; Ha: μ≠33 Let the parameter μ be used to represent the mean. The null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H0 is μ=33. The alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33. Question 2 1/1 points The answer choices below represent different hypothesis tests. Which of the choices are right- tailed tests? Select all correct answers. That is correct! • H0:X≥17.1, Ha:X<17.1 • • H0:X=14.4, Ha:X≠14.4 • • H0:X≤3.8, Ha:X>3.8 • • H0:X≤7.4, Ha:X>7.4 • • H0:X=3.3, Ha:X≠3.3 • Answer Explanation Correct answer: H0:X≤3.8, Ha:X>3.8 H0:X≤7.4, Ha:X>7.4 The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight, x¯=3.7. The sample the chef uses is 14 meatballs, so n=14. She knows the standard deviation of the meatballs, σ=0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=3.7−40.514√≈−0.30.134≈−2.24 So, the test statistic for this hypothesis test is z0=−2.24. • • • • Question 5 1/1 points What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=1.74? (Do not round your answer; compute your answer using a value from the table below.) z1.51.61.71.81.90.000.9330.9450.9550.9640.9710.010.9340.9460.9560.9650.9720.020.9360.947 0.9570.9660.9730.030.9370.9480.9580.9660.9730.040.9380.9490.9590.9670.9740.050.9390.951 0.9600.9680.9740.060.9410.9520.9610.9690.9750.070.9420.9530.9620.9690.9760.080.9430.954 0.9620.9700.9760.090.9440.9540.9630.9710.977 That is correct! 0 point 0 4 1$$ 0 point 0 4 1 - correct Answer Explanation Correct answers: • 0 point 0 4 1 $0.041$ • The p-value is the probability of an observed value of z=1.74 or greater if the null hypothesis is true, because this hypothesis test is right-tailed. This probability is equal to the area under the Standard Normal curve to the right of z=1.74. A standard normal curve with two points labeled on the horizontal axis. The mean is labeled at 0.00 and an observed value of 1.74 is labeled. The area under the curve and to the right of the observed value is shaded. Using the Standard Normal Table, we can see that the p-value is equal to 0.959, which is the area to the left of z=1.74. (Standard Normal Tables give areas to the left.) So, the p-value we're looking for is p=1−0.959=0.041. Question 6 1/1 points Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds? Accept or reject the hypothesis given the sample data below. • H0:μ=8.2 seconds; Ha:μ<8.2 seconds • α=0.04 (significance level) • z0=−1.75 • p=0.0401 That is correct! Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. Reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. Reject the null hypothesis because the value of z is negative. Reject the null hypothesis because |−1.75|>0.04. Do not reject the null hypothesis because |−1.75|>0.04. Answer Explanation Correct answer: Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. In making the decision to reject or not reject H0, if α>p-value, reject H0 because the results of the sample data are significant. There is sufficient evidence to conclude that H0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct. If α≤p-value, do not reject H0. The results of the sample data are not significant, so there is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct. In this case, α=0.04 is less than or equal to p=0.0401, so the decision is to not reject the null hypothesis. • • • QUESTION 7 1/1 POINTS A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test? That is correct! Ha:p ≠ 0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve: That is correct! $$P-value=0.124 Answer Explanation Correct answers: • $\text{P-value=}0.124$P-value=0.124 Here are the steps needed to calculate the p-value for a hypothesis test for a proportion: 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 1. Determine if the hypothesis test is left tailed, right tailed, or two tailed. 2. Compute the value of the test statistic. 3. If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0 If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0 If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve For this example, the test is a two tailed test and the test statistic, rounding to two decimal places, is z=0.1033−0.120.12(1−0.12)900−−−−−−−−−−−−√≈−1.54. Thus the p-value is the area under the Standard Normal curve to the left of a z-score of -1.54, plus the area under the Standard Normal curve to the right of a z-score of 1.54. From a lookup table of the area under the Standard Normal curve, the corresponding area is then 2(0.062) = 0.124. QUESTION 10 1/1 POINTS 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 An economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%. To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car Of these 750 people, 513 indicate that they do plan to purchase an electric vehicle. The following is the setup for this hypothesis test: H0:p=0.65 Ha:p>0.65 In this example, the p-value was determined to be 0.026. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%.) That is correct! The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim. Answer Explanation Correct answer: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. To come to a conclusion and interpret the results for a hypothesis test for proportion using the P- Value Approach, the first step is to compare the p-value from the sample data with the level of significance. is y=50+45x. What are the independent and dependent variables? What is the y-intercept and the slope? That is correct! The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer. John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50. The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50. Answer Explanation Correct answer: The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer. John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45. The independent variable (x) is the amount of time John fixes a computer because it is the value that changes. He may work different amounts per computer, and his earnings are dependent on how many hours he works. This is why the amount, in dollars, John earns for a computer is the dependent variable (y). The y-intercept is 50 (b=50). This is his one-time fee. The slope is 45 (a=45). This is the increase for each hour he works. QUESTION 13 1/1 POINTS Ariana keeps track of the amount of time she studies and the score she gets on her quizzes. The data are shown in the table below. Which of the scatter plots below accurately records the data? Hours studying Quiz score 1 5 2 5 3 7 4 9 5 9 That is correct! A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 10 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; left- parenthesis 3 comma 7 right-parentheses; left-parenthesis 4 comma 9 right-parentheses; left- parenthesis 5 comma 9 right-parentheses. All values are approximate. A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 12 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; left- parenthesis 3 comma 8 right-parentheses; left-parenthesis 4 comma 8 right-parentheses; left- parenthesis 5 comma 11 right-parentheses. All values are approximate. Answer Explanation Correct answer: A scatterplot has a horizontal axis labeled Hours studying from 0 to 6 in increments of 1 and a vertical axis labeled Quiz score from 0 to 10 in increments of 2. The following points are plotted: left-parenthesis 1 comma 5 right-parentheses; left-parenthesis 2 comma 5 right-parentheses; left- parenthesis 3 comma 7 right-parentheses; left-parenthesis 4 comma 9 right-parentheses; left- parenthesis 5 comma 9 right-parentheses. All values are approximate. The values for hours studying correspond to x-values, and the values for quiz score correspond to y-values. Each row of the table of data corresponds to a point (x,y) plotted in the scatter plot. For example, the first row, 1,5, corresponds to the point (1,5). Doing this for every row in the table, we find the scatter plot should have points (1,5), (2,5), (3,7), (4,9), and (5,9). QUESTION 14 1/1 POINTS Data is collected on the relationship between time spent playing video games and time spent with family. The data is shown in the table and the line of best fit for the data is y^=−0.27x+57.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables. Video Games (Minutes) 306090120 Time with Family (Minutes) 50403525 According to the line of best fit, the predicted number of minutes spent with family for someone who spent 95 minutes playing video games is 31.85. Is it reasonable to use this line of best fit to make the above prediction? That is correct! The estimate, a predicted time of 31.85 minutes, is unreliable but reasonable. The estimate, a predicted time of 31.85 minutes, is both unreliable and unreasonable. The estimate, a predicted time of 31.85 minutes, is both reliable and reasonable. The estimate, a predicted time of 31.85 minutes, is reliable but unreasonable. Answer Explanation Correct answer: The estimate, a predicted time of 31.85 minutes, is both reliable and reasonable. The data in the table only includes video game times between 30 and 120 minutes, so the line of best fit gives reasonable predictions for values of x between 30 and 120. Since 95 is between these values, the estimate is both reliable and reasonable. QUESTION 15 0/1 POINTS Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply. 1.0 751 0.5 267 0.8 229 0.5 552 HelpCopy to ClipboardDownload CSV That is correct! $$r= 0.18 Answer Explanation Correct answers: • $\text{r= }0.18$r= 0.18 The correlation coefficient can be calculated easily with Excel using the built-in CORREL function. 1. Open the accompanying data set in Excel. 2. In an open cell, type "=CORREL(A2:A31,B2:B31)", and then hit ENTER. You could label the result of this cell by writing "Correlation coefficient" or "r" in an adjacent open cell. The correlation coefficient, rounded to two decimal places, is r≈0.18. QUESTION 18 0/1 POINTS The weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars’ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find the best fit linear regression equation, where weight is the explanatory variable. Round the slope and intercept to three decimal places. Weight Mileage 30.0 32.2 20.0 56.0 20.0 46.2 45.0 19.5 40.0 23.6 45.0 16.7 25.0 42.2 55.0 13.2 17.5 65.4 HelpCopy to ClipboardDownload CSV That's not right. y = $$1.181 x + $$71.374 Answer Explanation y = 1$$ x + 2$$ Correct answers: • 1$-1.181$−1.181 • 2$71.374$71.374 To find the best fit for the given data, use Excel. 1. Open Excel. Enter the values of weight in column A and mileage in column B. Highlight all the cells containing the data. 2. From the Insert tab, select Scatter. Use Scatter with only Markers, the first type of scatter chart. A simple plot is shown. 3. To add the linear fit to the graph, click anywhere inside the graph area. Select the Layout tab from the Chart Tools. Click on the Trendline icon and select the Linear Trendline option. The line of best fit is added to the graph. 4. For the equation of the line of best fit, click on Trendline and select More Trendline Options.... 5. Check the Display Equation on chart box. The equation of line of best fit is shown on the graph. 6. To change the number of decimal places in the trendline equation, right-click on the equation for the trendline and select Format Trendline Label.... 7. Select Number under Category, change the number of decimal places to 3, and click Close. Thus, the equation of line of best fit with slope and intercept rounded to three decimal places is yˆ=−1.181x+71.374. QUESTION 19 1/1 POINTS A doctor notes her patient's temperature in degrees Fahrenheit every hour to make sure the patient does not get a fever. What is the level of measurement of the data? That is correct! nominal ordinal interval ratio Answer Explanation Correct answer: interval This is interval data because degrees Fahrenheit is a numerical scale where differences are meaningful. However, because Fahrenheit does not have a true zero value, it is not ratio data. QUESTION 22 0/1 POINTS As a member of a marketing team, you have been tasked with determining the number of DVDs that people have rented over the past six months. You sample twenty adults and decide that the best display of data is a frequency table for grouped data. Construct this table using four classes. 15,31,28,19,14,18,28,19,10,19,10,24,14,18,24,27,10,18,16,23 That's not right. Lower Class Limit Upper Class Limit Fr $$10 $$15 $$ $$16 $$21 $$ $$22 $$27 $$ $$18 $$33 $$ Answer Explanation Lower Class Limit Upper Class Limit Fr 1$$ 2$$ 3$ 4$$ 5$$ 6$ 7$$ 8$$ 9$ 10$$ 11$$ 12 Correct answers: • 1$10$10 • 2$15$15 • 3$6$6 • 4$16$16 • 5$21$21 • 6$7$7 • 7$22$22 • 8$27$27 • 9$4$4 • 10$28$28 • 11$33$33 • 12$3$3 Note that the data is not ordered and that we have been asked to use 4 classes. To determine the class width, use the formula: Max Value−Min ValueNumber of Classes=31−104=5.25. Since this value is not an integer, round to 6. A histogram has a vertical axis labeled Frequency and has a horizontal axis that measures six categories of rainbow trout weight (in pounds). Reading from left-to-right, the weight and frequency of each category are: 4.5 to 6.5 has frequency of 4, 6.5 to 8.5 has frequency 5, 8.5 to 10.5 has frequency 7, 10.5 to 12.5 has frequency 3, 12.5 to 14.5 has frequency 1, 14.5 to 16.5 has frequency 2. That is correct! $$greater than 12.5 but less than 14.5 Answer Explanation Correct answers: • $\text{greater than }12.5\ \text{but less than }14.5$greater than 12.5 but less than 14.5 The range 12.5−14.5 has the lowest bar in the histogram, which means that this range of values also has the lowest frequency. Therefore, 1 visitor caught a rainbow trout that weighed greater than 12.5 but less than 14.5 pounds. QUESTION 24 1/1 POINTS Describe the shape of the given histogram. A histogram has a horizontal axis from 0 to 16 in increments of 2 and a vertical axis labeled Frequency from 0 to 10 in increments of 2. The histogram contains vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the frequency is listed second: 0, 0; 1, 0; 2, 6; 3, 6; 4, 7; 5, 6; 6, 6; 7, 6; 8, 7; 9, 6; 10, 6; 11, 6; 12, 6; 13, 7; 14, 0; 15, 0. That is correct! uniform unimodal and symmetric unimodal and left-skewed unimodal and right-skewed bimodal Answer Explanation Correct answer: uniform All the bars in a uniform histogram are about the same height. QUESTION 25 1/1 POINTS The bar graph below shows the number of boys and girls in different classes. That's not right. From the data, the number of TVs doubled from a square footage of 8.5 and 10. From the data, there is a steady decrease in the square footage and number of TVs. From the data, there is a steady increase in the square footage and number of TVs. From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. Answer Explanation Correct answer: From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. Given the line graph, at a square footage of 8.5, the number of TVs is 3. At a square footage of 10, the number of TVs is also 3. Therefore, when the square footage is between 8.5 and 10, the number of TVs remains the same. Your answer: From the data, there is a steady increase in the square footage and number of TVs. This response is not correct. While most of the line is increasing, the number of TVs remains the same between a square footage of 8.5 and 10. QUESTION 27 1/1 POINTS Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below. 16,14,14,21,15 Find the mean boxes sold. That is correct! $$mean=16 boxes Answer Explanation Correct answers: • $\text{mean=}16\text{ boxes}$mean=16 boxes Remember that the mean is the sum of the numbers divided by the number of numbers. There are 5 numbers in the list. So we find that the mean boxes sold is QUESTION 28 1/1 POINTS Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. 20,46,19,14,42,26,33 That is correct! $$median=26 thousands of dollars Answer Explanation Correct answers: • $\text{median=}26\text{ thousands of dollars}$median=26 thousands of dollars It helps to put the numbers in order. 14,19,20,26,33,42,46 Now, because the list has length 7, which is odd, we know the median number will be the middle number. In other words, we can count to item 4 in the list, which is 26. So the median price (in thousands of dollars) of randomly selected trucks at a car dealership is 26. QUESTION 29 1/1 POINTS Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears. 3,12,3,11,5,5,3,10,12 That is correct! $$mode=3 cards Answer Explanation Correct answers: • $\text{mode=}3\text{ cards}$mode=3 cards If we count the number of times each value appears in the list, we get the following frequency table: Value Frequency 3 3 5 2 The data are skewed to the right. The data are symmetric. Answer Explanation Correct answer: The data are symmetric. Note that the histogram appears to be roughly symmetric. So the data are symmetric. QUESTION 31 1/1 POINTS Which of the data sets represented by the following box and whisker plots has the smallest standard deviation? Four horizontal box-and-whisker plots share a vertical axis with the classes D, C, B, and A and a horizontal axis from 0 to 120 in increments of 20. The box-and-whisker plot above the class label A has the following five-number summary: 44, 69, 77, 82, and 112. The box-and-whisker plot above the class label B has the following five-number summary: 19, 64, 78, 87, and 121. The box-and-whisker plot above the class label C has the following five-number summary: 60, 72, 75, 80, and 92. The box-and-whisker plot above the class label D has the following five-number summary: 2, 63, 77, 92, and 138. All values are approximate. That is correct! A B C D Answer Explanation Correct answer: C Remember that the standard deviation is a measure of how spread out the data is. If the values are concentrated around the mean, then a data set has a lower standard deviation. A box and whisker plot with short whiskers and a short box has values that are less spread out, and hence has a smaller standard deviation. QUESTION 32 1/1 POINTS The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation. Correct answer: At the 0.01 level of significance, the coin is likely not a fair coin. The results of the experiment are significant at the 0.01 level of significance. This means the probability that the outcome was the result of chance is 0.01 or less. Because of this, we can be fairly confident, but not certain, that the coin is not a fair coin. QUESTION 34 1/1 POINTS Is the statement below true or false? Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. That is correct! True False Answer Explanation Correct answer: True Independent is defined as the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs. QUESTION 35 1/1 POINTS Of the following pairs of events, which pair has mutually exclusive events? That is correct! rolling a sum greater than 7 from two rolls of a standard die and rolling a 4 for the first throw drawing a 2 and drawing a 4 with replacement from a standard deck of cards rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll drawing a red card and then drawing a black card with replacement from a standard deck of cards Answer Explanation Correct answer: rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll Mutually exclusive events are events that cannot occur together. In this case, rolling a sum of 9 from two rolls of a standard die and rolling 2 for the first roll are two events that cannot possibly occur together. QUESTION 36 1/1 POINTS Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains. StudentsgotothebeachdonotgotothebeachTotalgotothemountains48donotgotothemountains21Tota l3695 That is correct! $$10 Answer Explanation Correct answers: • $10$10 By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the row of totals in the table, we know that the unknown number plus 48 is 95, so the missing number must be 47. Continuing in this way, we can fill in the entire table: StudentsgotothebeachdonotgotothebeachTotalgotothemountains103848donotgotothemountains2 62147Total365995 From this, we can see that the number of students who both go to the beach and go to the mountains is 10. QUESTION 37 1/1 POINTS A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x¯=77, with a margin of error of 10. Construct a confidence interval for the mean score (out of 100 points) on the final exam. That is correct! That's not right. • Value Frequency 5 1 6 2 7 10 8 11 9 17 10 17 11 15 12 12 13 7 14 7 15 0 MATH 225N Week 8 Final Exam (Version 1 & 2) 16 1 • • Value Frequency 5 1 6 3 7 8 8 10 9 13 10 26 11 14 12 12 13 8 14 3 15 1 MATH 225N Week 8 Final Exam (Version 1 & 2) 16 1 • • Value Frequency 12 1 13 1 14 3 15 6 16 23 17 29 18 19 19 15 20 3 • • MATH 225N Week 8 Final Exam (Version 1 & 2) 7 2 Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values: Value Frequency 12 1 13 1 14 3 15 6 16 23 17 29 18 19 19 15 20 3 MATH 225N Week 8 Final Exam (Version 1 & 2) And the following is right skewed because of its concentration of small values with many larger values: Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 7 2 The other frequency tables are more balanced and symmetrical. Your answer: Value Frequency 5 1 6 3 MATH 225N Week 8 Final Exam (Version 1 & 2) 7 8 8 10 9 13 10 26 11 14 12 12 13 8 14 3 15 1 16 1 The data in this table is roughly symmetrical about 10. Value Frequency 12 1 13 1 14 3 MATH 225N Week 8 Final Exam (Version 1 & 2) the group that received the anxiety-reduction pill the psychological study all the people in the study the group that received the inert pill Answer Explanation Correct answer: the group that received the inert pill When the experimental units are people, applying treatments that should be inert can actually have effects. So the group that received the inert pill received the placebo. QUESTION 43 1/1 POINTS Which of the following results in the null hypothesis μ≥38 and alternative hypothesis μ<38? That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) A fitness center claims that the mean amount of time that a person spends at the gym per visit is at most 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is more than 38 minutes. Answer Explanation Correct answer: A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. Consider each of the options. The scenario in option B has the null hypothesis μ≥38 based on the words "fewer than" and the fact that the null hypothesis is always stated with some form of equality. QUESTION 44 1/1 POINTS True or False: The more shoes a manufacturer makes, the more shoes they sell. That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) True False Answer Explanation Correct answer: False In supply and demand, a company doesn't make a product hoping that someone will buy them, they have a Demand first for their product and then, they produce more of that given product. QUESTION 45 1/1 POINTS Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total6267 That is correct! $$34 Answer Explanation Correct answers: • $34$34 MATH 225N Week 8 Final Exam (Version 1 & 2) H0:X=13.2, Ha:X≠13.2 • • H0:X=17.8, Ha:X≠17.8 • Answer Explanation Correct answer: H0:X≥19.7, Ha:X<19.7 H0:X≥11.2, Ha:X<11.2 Remember the forms of the hypothesis tests. • Right-tailed: H0:X≤X0, Ha:X>X0. • Left-tailed: H0:X≥X0, Ha:X<X0. • Two-tailed: H0:X=X0, Ha:X≠X0. So in this case, the left-tailed tests are: • H0:X≥11.2, Ha:X<11.2 • H0:X≥19.7, Ha:X<19.7 • • • • Question 47 · 1/1 points Assume the null hypothesis, H0, is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario. That is correct! MATH 225N Week 8 Final Exam (Version 1 & 2) Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does. Answer Explanation Correct answer: Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when Jacob thinks he does not earn enough money when he really does. • • • • Question 48 · 1/1 points Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. MATH 225N Week 8 Final Exam (Version 1 & 2) A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A. That is correct! • A has the larger mean. • • B has the larger mean. • • The means of A and B are equal. MATH 225N Week 8 Final Exam (Version 1 & 2) Answer Explanation Correct answer: Suppose Hugo types 56 words per minute in a typing test on Wednesday. The z-score when x=56 is −0.75. This z-score tells you that x=56 is 0.75 standard deviations to the left of the mean, 62. The z-score can be found using the formula z=x−μσ=56−628=−68≈−0.75 A negative value of z means that that the value is below (or to the left of) the mean, which was given in the problem as μ=62 words per minute in a typing test. The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. So, typing 56 words per minute is 0.75 standard deviations away from the mean. • • • • Question 50 · 1/1 points The following frequency table summarizes a set of data. What is the five-number summary? Value Frequency 1 6 2 2 3 1 4 1 8 1 9 1 10 1 16 6 20 3 21 1 23 1 24 1 25 1 27 1 MATH 225N Week 8 Final Exam (Version 1 & 2) That is correct! Min Q1 Median Q3 Max 1 2 16 20 27 Min Q1 Median Q3 Max 11 33 2020 2222 27 Min Q1 Median Q3 Max $_1$_ $_2$_ $_6$_ $_20$_ $_27$_ Min Q1 Median Q3 Max $_1$_ $_4$_ $_5$_ $_16$_ $_27$_ Min Q1 Median Q3 Max $_1$_ $_7$_ $_8$_ $_22$_ $_27$_ Answer Explanation Correct answer: Min Q1 Median Q3 Max $_1$_ $_2$_ $_16$_ $_20$_ $_27$_ We can immediately see that the minimum value is $_1$_ and the maximum value is $_27$_. If we add up the frequencies in the table, we see that there are $_27$_ total values in the data set. Therefore, the median value is the one where there are $_13$_ values below it and $_13$_ values above it. By adding up frequencies, we see that this happens at the value $_16$_, so that is the median. Now, looking at the lower half of the data, there are $_13$_ values there, and so the median value of that half of the data is $_2$_. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is $_20$_. $_\color{blue}{1}$_, $_1$_, $_1$_, $_1$_, $_1$_, $_1$_, $_\color{blue}{2}$_, $_2$_, $_3$_, $_4$_, $_8$_, $_9$_, $_10$_, $_\color{blue}{16}$_, $_16$_, $_16$_, $_16$_, $_16$_, $_16$_, $_20$_, $_\color{blue}{20}$_, $_20$_, $_21$_, $_23$_, $_24$_, $_25$_, MATH 225N Week 8 Final Exam (Version 1 & 2) $_\color{blue}{27}$_ So, the five-number summary is Min Q1 Median Q3 Max $_1$_ $_2$_ $_16$_ $_20$_ $_27$_