MATH 225N Week 2 Statistics Quiz – Question and Answers, Exercises of Mathematics

Download MATH 225N Week 2 Statistics Quiz – Question and Answers and more Exercises Mathematics in PDF only on Docsity! That is correct! MATH 225N Week 2 Statistics Quiz – Question and Answers Question 1 A company has developed a wristband for monitoring blood sugar levels without requiring direct blood samples. It is interested in demonstrating the accuracy of the device for governmental approval and has decided to test the claim "The glucose level reported by the wristband is within 10% of a standard blood test result." Which of the following data collection processes would be appropriate? Select only one answer choice. Choose a random sample of employees at lunchtime and measure their blood sugar using both the wristband and a standard blood test. Choose a random sample of people from the local area and random times throughout the day and measure their blood sugar using both the wristband and a standard blood test. Choose a random sample of people from the local area and random times and measure their blood sugar using the wristband. Choose another random sample of people and random times and measure their blood sugar using the standard blood test. Go to a hospital and have the doctors choose a random sample of patients to be tested at random times using both the wristband and the standard blood test. Answer Explanation Correct answer: To compare the wristband to the standard blood test, both methods should be used to measure the blood sugar of the same person at the same time. The people chosen should be random, and the time of measurement should be random to help eliminate the effects of any confounding variables. FEEDBACK • • • • Content attribution- Opens a dialog Choose a random sample of people from the local area and random times throughout the day and measure their blood sugar using both the wristband and a standard blood test. the physicians the group that received the drug for headache the group that received the drug with no therapeutic effect all of the people in the study Answer Explanation Correct answer: the group that received the drug with no therapeutic effect When the experimental units are people, applying treatments that should be inert can actually have effects. In this study, the drug with no therapeutic effects is the placebo, so the group that receives that drug receives the placebo. FEEDBACK • • • • Content attribution- Opens a dialog Question 4 Matthew has created a survey to test whether or not gender has any effect on political party associations. What is the explanatory variable in this situation? the number of people surveyed political party associations gender That is correct! That is correct! none of the above Answer Explanation Correct answer: gender The explanatory variable is the independent variable, which is the variable that is changed to determine its effect on a dependent variable. In this case the explanatory variable is gender. FEEDBACK • • • • Content attribution- Opens a dialog Question 5 Is the statement below true or false? Continuous data are the type of quantitative data that is the result of measuring. True False Answer Explanation Correct answer: True Continuous data are defined as the type of quantitative data that is the result of measuring. FEEDBACK • • • • Content attribution- Opens a dialog Question 6 A doctor notes her patient's temperature in degrees Fahrenheit That is correct! Correct answer: the 200 randomly selected students A sample is a specific subset of the entire group of individuals being studied. In this case, the sample is the 200 randomly selected students. FEEDBACK • • • • Content attribution- Opens a dialog Question 8 True or False? In reference to different sampling methods, systematic sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group. True False Answer Explanation Correct answer: Systematic sampling includes the steps: list the members of the population; use simple random sampling to select a starting point in the population; let k = (number of individuals in the population)/(number of individuals needed in the sample); choose every kth individual in the list starting with the one that was randomly selected. Stratified sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group. Your answer: FEEDBACK • • • • True False That's not right. Content attribution- Opens a dialog Question 9 While standing on a highway overpass, Jennifer wonders what proportion of the vehicles that pass on the highway below are trucks. The highway has 4 lanes running in each direction. Jennifer is only interested in the proportion of vehicles that pass over the course of the hour that she spends there. Which of the following sampling methods would be best for Jennifer to employ? Answer Explanation Lower Class Limit Upper Class Limit $$10 $$14 $$15 $$19 $$20 $$24 $$25 $$30 Correct answers: • • • 1$10$10 2$15$15 3$6$6 Lower Class Limit Upper Class Limit 1$$ 2$$ 4$$ 5$$ 7$$ 8$$ 10$$ 11$$ 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. Use the minimum value, 10, for the lower class limit of the first class. To find all other lower class limits, add the class width, 6. For example, the second lower class limit would be: 10+6=16. Lower Class Limit Upper Class Limit Frequen cy 10 16 22 28 • • • • • • • • • 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 shown below. Complete the cumulative relative frequency table. Data Value Relative Frequency Cumulative Relative Frequency 1 0.12 $$0.12 Data Value Relative Frequency Cumulative Relative Frequency 2 0.23 $$0.35 3 0.34 $$0.69 4 0.31 $$1.0012 Answer Explanation Data Value Relative Frequency Cumulative Relative Frequency 1 0.12 1$$ 2 0.23 2$$ 3 0.34 3$$ 4 0.31 4$$ Correct answers: The cumulative relative frequency is the accumulation of the previous relative frequencies. To find the values in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. • 1$0.12$0.12 • 2$0.35$0.35 • 3$0.69$0.69 • 4$1.00$1.00 Data Value Relative Frequency Cumulative Relative Frequency 1 0.12 0.12 That is correct! $$greater than 12.5 but less than 14.5 That is correct! Answer Explanation Correct answers: The range 12.5−14.5 has the lowest bar in the histogram, which means that this range of values also has the lowest frequency. Therefore, 1 visitor caught a rainbow trout that weighed greater than 12.5 but less than 14.5 pounds. FEEDBACK • • • • Content attribution- Opens a dialog Question 13 Describe the shape of the given histogram. A histogram has a horizontal axis from 0 to 16 in increments of 2 and a vertical axis labeled Frequency from 0 to 10 in • $\text{greater than }12.5\ \text{but less than }14.5$greater than 12.5 but less than 14.5 increments of 2. The histogram contains vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the frequency is listed second: 0, 0; 1, 0; 2, 6; 3, 6; 4, 7; 5, 6; 6, 6; 7, 6; 8, 7; 9, 6; 10, 6; 11, 6; 12, 6; 13, 7; 14, 0; 15, 0. • 1$12$12 • 2$12$12 • 3$6$6 There are 1$$ values in the data set which are greater than or equal to 10 and less than or equal to 19. There are 2$$values in the data set which are greater than or equal to 30 and less than or equal to 39. There are 3$$ values in the data set which are greater than or equal to 20 and less than or equal to 29. Correct answers: Remember that every entry in the leaf column corresponds to a value in the data set. To see about values in a certain range, find the stem for the values you want. For instance, there are 12 entries in the leaf column of the first row (with stem 1), so there are 12 values in the data set which are greater than or equal to 10 and less than or equal to 19. FEEDBACK • • • • Content attribution- Opens a dialog Question 15 The bar graph below shows the number of boys and girls in different classes. A bar graph has a horizontal axis labeled Classes and a vertical axis labeled Students from 0 to 16 in increments of 2. There are two vertical bars above each horizontal axis label, with the bar on the left representing Boys and the bar on the right representing Girls. The bars have heights as follows, with the horizontal axis label listed first and the bar heights listed second from left to right: Mrs. Brown, 10 and 15; Ms. James, 11 and 12. How many total students are in Ms. James's class? Do not include the units in your answer. A line graph has an x-axis labeled Square Footage (in hundreds of feet) in increments of one, and a y-axis labeled Number of TV's in increments of one. Beginning at the point That is correct! start parentheses 6,2 end parentheses, a line increases to the point start parentheses 8.5,3 end parentheses. The line remains constant to the point start parentheses 10,3 end parentheses. The line then increases, passing through the point start parentheses 12,5 end parentheses and continues increasing until it reaches the point start parentheses 16,6 end parentheses. 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: 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. FEEDBACK • • From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same. • • Content attribution- Opens a dialog Question 17 Ashley is reviewing past monthly credit card statements. The statements are summarized in the relative frequency table below. What is the cumulative relative frequency of credit card statements that are $1245 or less? The cumulative relative frequency is the accumulation of the previous relative frequencies. To find any missing number in the cumulative relative frequency column of a table, add the relative frequencies in the previous column for the corresponding row and all previous rows. Statement Balance Relative Frequency Cumulative Relative Frequency 838−939 0.10 0.10 940−1041 0.15 0.25 1042−1143 0.20 0.45 1144−1245 0.05 0.50 1246−1347 0.25 0.75 1348−1449 0.25 1.00 The Cumulative Relative Frequency of credit card statements that are $1245 or less is the sum of the first four Relative Frequencies: 0.10+0.15+0.20+0.05=0.50 FEEDBACK • • • • Content attribution- That's not right. Opens a dialog Content attribution- Opens a dialog Question 19 An English professor asks her students who their favorite character is in the novel they are reading. What is the level of measurement of the data? nomi nal ordin al interv al ratio Answer Explanation Correct answer: nominal This is nominal data because the characters do not have an order to them. Even though a person may have a personal preference, there is no ranking that is universal. Your answer: ratio Data measured with a ratio scale level is data with a starting point that can be ordered. The differences in the data values have meaning, and ratios can be calculated. FEEDBACK • • • • Content attribution- Opens a dialog Question 20 Jessica is keeping track of her favorite stock's price. The line graph below shows the data. That is correct! By looking horizontally from the vertical axis value of 10, we can see that the corresponding value of time is 2. FEEDBACK • • • • Content attribution- Opens a dialog Question 21 A set of data is summarized by the stem and leaf plot below. Stem1234Leaf0011222344466770233444555567899123456 6 7789011223333444555799 The value 10 appears $$2 time(s) in the data set. The value 14 appears $$3 time(s) in the data set. Answer Explanation The value 10 appears 1$$ time(s) in the data set. The value 14 appears 2$ $ time(s) in the data set. Correct answers: To find the number of times 14 appears in the data set, note that the stem (the part of the number before the last digit) is 1, and the leaf is 4. In the row for the stem 1, the leaf 4 occurs 3 times, so 14 appears 3 times in the data set. • 1$2$2 • 2$3$3 Similarly for the other answer. FEEDBACK • • • • Content attribution- Opens a dialog Question 22 Describe the shape of the given histogram. A histogram has a horizontal axis from 0 to 16 in increments of 2 and a vertical axis labeled Frequency from 0 to 10 in increments of 2. The histogram contains vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the frequency is listed second: 0, 0; 1, 1; 2, 1; 3, 2; 4, 3; 5, 5; 6, 7; 7, 8; 8, 8; 9, 6; 10, 5; 11, 3; 12, 2; 13, 2; 14, 1; 15, 0. 7 9 8 1 9 6 10 4 Give your answer as a single number. For example if you found the number of values was 23, you would enter 23. Answer Explanation Correct answers: • $20$20 The relevant values are highlighted in the table below. Value Frequency 0 7 1 5 2 3 3 2 4 3 5 5 6 0 7 9 8 1 9 6 10 4 Summing the frequencies for these values, we find 9+1+6+4=20 FEEDBACK • • • $$20 That is correct! • Content attribution- Opens a dialog Question 24