Statistics Final Exam 2024-2025. Questions and Correct, Verified Answers. Graded A+, Exams of Statistics

Download Statistics Final Exam 2024-2025. Questions and Correct, Verified Answers. Graded A+ and more Exams Statistics in PDF only on Docsity! Statistics Final Exam 2024-2025. Questions and Correct, Verified Answers. Graded A+ 5, 3, 7, 6, 6, 2, 5, 3, 4, 7 Using the same data as the previous two questions, construct a box-and-whiskers plot. What you type in this answer box will not be graded. - ANSQuestion 5 image from document with pics from test 1 A 1992 Roper poll found that 22% of Americans say that the Holocaust may not have happened. The actual question asked in the poll was, "Does it seem possible or impossible to you that the Nazi extermination of the Jews never happened?" Explain why the results cannot be trusted. - ANSThe main issue is that the survey question is confusing and may have caused participants to answer the opposite of what they intended. A basketball player makes 66% of his free throws. Let X represent the number of free throws made in three tries. The probability distribution for the number of free throws he makes in three attempts is summarized in the following table:(Image 5) What is the expected value of the number of free throws he will make? Do not round. - ANS1.978 A basketball player makes 66% of his free throws. Let X represent the number of free throws made in three tries. The probability distribution for the number of free throws he makes in three attempts is summarized in the following table:(Image 5) What is the probability that he will make at least 1 free throw? - ANS0.96 A basketball player makes 66% of his free throws. Let X represent the number of free throws made in three tries. The probability distribution for the number of free throws he makes in three attempts is summarized in the following table:(Image 5) What is the standard deviation of the number of free throws he will make? Round your answer to three decimal places. - ANS0.820 A college randomly selects 20 professors to attend a conference. Is this a simple random sample, stratified random sample, cluster sample, or convenience sample? - ANSSimple random sample A college's professors are 45% male and 55% female. The college then randomly selects 9 of the male professors and 11 of the female professors to attend. Is this a simple random sample, stratified random sample, cluster sample, or convenience sample? - ANSStratified random sample A company has three divisions and three conference rooms for meetings. To keep track of the use of their facilities, for each meeting held in the company, they record which division is holding the meeting, the room for the meeting, and the length of time for the meeting. Is the division qualitative or quantitative? Is the room qualitative or quantitative? Is the length of time qualitative or quantitative? - ANSQualitative, Qualitative, Quantitative A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. Previous research has shown the standard deviation to be 1.50. The researchers wish the margin of error to be no larger than 0.4 for a 90% confidence interval. What sample size is needed to accomplish this? - ANS39 A national health survey of 1483 U.S. adults during 2014 revealed that 668 had never smoked cigarettes. Find a 95% large-sample confidence interval for the proportion of U.S. adults that had never smoked cigarettes. Enter the lower bound in the first answer blank and the upper bound in the second answer blank. Round your answers to the nearest thousandth. - ANSAnswer for blank #1: 0.425 Answer for blank #2: 0.476 A political party sends a mail survey to 1450 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 482 are returned, and of these, only 211 say they're satisfied with the President's job performance. What is a reason the survey results cannot be trusted? (STUDY TYPES OF BIAS) - ANSThese survey results cannot be trusted because they contain voluntary bias meaning that people chose to fill them out. Often times in these type of scenarios the far majority of people filling out these surveys feel strongly about the issue whatever their stance may be. This leads to the population not accurately being represented since the people who don't care as much about the issue aren't surveyed since it heavily relies on volunteers. A political party sends a mail survey to 1450 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 482 are returned, and of these, only 211 say they're satisfied with the President's job performance. What is the sample size? - ANS482 A political party sends a mail survey to 1450 randomly selected registered voters in a community. The survey asks respondents to give an opinion about the job performance of the current President. Of the 1500 surveys sent out, 482 are returned, and of these, only 211 say they're satisfied with the President's job performance. What should be the population of this study? Be specific. - ANSThe population would be registered voters in that specific community. According to the National Institute on Alcohol Abuse and Alcoholism, 45% of college students nationwide engage in binge drinking behavior. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. Using a 90% confidence interval, what sample size is needed if she wants the margin of error to be less than 3 percentage points? - ANS745 Assume that event A occurs with probability 0.03 and event B occurs with probability 0.17. Assume that A and B are mutually exclusive events. What is the probability that both events occur? - ANS0 Assume that event A occurs with probability 0.39 and event B occurs with probability 0.26. Assume that A and B are mutually exclusive events. What is the probability that A or B occurs? - ANS0.65 Assume that event A occurs with probability 0.47 and event B occurs with probability 0.44. Assume that A and B are mutually exclusive events. What is the probability that B does not occur? - ANS0.56 Based purely on the histogram (i.e. no calculations necessary), is there an outlier?(Image 1) Briefly explain why or why not. - ANSYes, 145-155, is an outlier. The substantial number of visitors are to the left of the outlier by a sizeable margin. Due to this large gap, 145-155 can be thought of as an outlier. Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. Give an estimated value of the correlation. - ANS0.93 Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. What is the explanatory variable in these studies? - ANSThe graduate's annual income Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. What is the response variable in these studies? - ANSAmount he or she would be willing to donate Colleges often rely heavily on raising money for an annual fund to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. Which variable goes on the y-axis of a scatterplot? - ANSAmount he or she would be willing to donate DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. Let μ1 be the mean nerve sensitivity for rats poisoned with DDT. Let μ2 be the mean nerve sensitivity for rats not poisoned with DDT. a. What are the appropriate hypotheses? b. If the p-value is 0.0084 and α is 0.01, give a conclusion in a complete sentence related to the scenario. - ANSa. Ho: µ1=µ2 Ha: µ1>µ2 b. Due to the p-value being less than the significance level or a, we reject the null hypothesis and there is sufficient evidence to suggest that DDT increases nerve sensitivity in rats. During the 1936 presidential election between Franklin D. Roosevelt and Alf Landon, the Literary Digest received 2.3 million mail-in surveys that it used to predict the results: a landslide in favor of Landon. Explain why the results cannot be trusted. - ANSThese results cannot be trusted because the people who sent in the survey are all subscribed to the Literary Digest which could generally have a biased view of the presidential election and not be completely unbiased in their reporting. Due to this, it would lead to the readers of the Literary Digest being a biased sample and more likely to choose one candidate over the other. Given the data below(Image 2), complete parts (a) and (b) on a sheet of paper that you will upload to the Test 1 Dropbox. What you type in the answer box will not be graded. (a) Construct a stem-and-leaf plot with a stem unit of 10 and a leaf unit of 1 (b) Construct a histogram using classes of size 10 with the first class being 10-19. - ANSQuestion 25 Test 1, but on the stem and leaf plot, the numbers need to be equally spaced Given the hypotheses H0: p = 0.10 Ha: p ≠ 0.10 and a random sample with 12 successes out of 180 individuals, do the following. a. Identify the test statistic as z, t, or χ2, and evaluate it. b. Find the p-value. - ANSa. The test statistic is z and z= -1.49 b. The p-value is 0.1362 Going back to the previous problem, if you weren't aware of the study done by the National Institute on Alcohol Abuse and Alcoholism, what value should you have used for the estimated proportion? According to the National Institute on Alcohol Abuse and Alcoholism, 45% of college students nationwide engage in binge drinking behavior. A college president wonders if the proportion of students enrolled at her college that binge drink is lower than the national proportion. Using a 90% confidence interval, what sample size is needed if she wants the margin of error to be less than 3 percentage points? - ANS0.5 If events A and B are independent, the probability of A is 0.03, and the probability of B is 0.86, find P (A | B). - ANS0.03 b. If the p-value is 0.0370 and α is 0.05, give a conclusion in a complete sentence related to the scenario. - ANSa. Ho: The level of education of someone and their smoking status are independent Ha: The level of education of someone and their smoking status are dependent b. Due to the p-value being less than the significance level or a, we reject the null hypothesis and there is sufficient evidence to suggest that education, and smoking status are dependent. List the conditions for the chi-square test. - ANSEvery expected value needs to be greater than 5. List the conditions for the population proportion test. - ANSrandom sample, at least 5 expected successes, and at least 5 expected failures List the conditions for the test of two population means. - ANStwo independent random samples, two normal sampling distributions Older children tend to be taller than younger children. Hence, the correlation between age and height in children must be negative.(T/F) - ANSFalse Older men tend to have lower muscle density. Hence, the correlation between age and muscle density in older men must be negative.(T/F) - ANSTrue Scores on a university exam are normally distributed with a mean of 77 and a standard deviation of 7. A score of at least 70 is required for a grade of at least C. Using the Empirical Rule, what percentage of students earned a grade of at least C? - ANS84 Scores on a university exam are normally distributed with a mean of 77 and a standard deviation of 7. A score of at least 70 is required for a grade of at least C. Using the Empirical Rule, what percentage of students scored between 63 and 91? - ANS95 State the conditions for a confidence interval for a population mean with a known population standard deviation. - ANSRandom sampling and normal distribution. State the conditions for a confidence interval for two population means. - ANSindependent and random samples, known σ1 and σ2, two normal sampling distributions State the conditions for a large-sample confidence interval for a population proportion. - ANSMore than 5 successes and 5 failures. Taller people tend to be heavier than shorter people, so the correlation between height and weight must be negative.(T/F) - ANSFalse The 137 horses in a study on enteroliths, a type of stone in the gut, were housed either in a small paddock, large paddock, stall, or in a grass pasture. Based on the bar chart below(Image 3), what is the approximate percent of horses living in a pasture? Round to the nearest tenth of a percent, and do not write the % sign. - ANS24.1 The American Veterinary Medical Association conducted a survey of veterinary clinics to estimate the proportion that do not treat large animals (cows, horses, etc.). Typically, 70% of the veterinary clinics in the world do not treat large animals. You wish to test whether American veterinary clinics are more likely to not provide this service. a. What are the appropriate hypotheses? b. If the p-value is 0.2097 and α is 0.01, give a conclusion in a complete sentence related to the scenario. - ANSa. Ho: p=0.7 Ha: p>0.7 b. Due to the p-value being greater than the significance level or a, we do not reject the null hypothesis and there is insufficient evidence to suggest that more than 70% of the veterinary clinics in America do not treat large animals. The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 120 gallons and standard deviation 9 gallons. a. (5 points) On a randomly-selected day, what is the probability that the grocery store sells at least 128 gallons? Round your answer to 3 decimal places. b. (5 points) Over a span of 10 days (assuming the randomness requirement is not violated), what is the probability that the grocery store sells an average of at least 128 gallons? Round your answer to 4 decimal places, if needed. - ANSa. 0.187 b. 0.0025 The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. Given that Jolyn has been waiting for 8 minutes, what is the probability that it takes Jolyn more than 11 minutes to wait? Round your answer to two decimal places if needed. - ANS0.25 The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. What is the expected wait time for Jolyn? - ANS9.5 The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. What is the probability that it takes between 9 and 11 minutes to wait? - ANS0.4 The amount of time it takes Jolyn to wait in line at the bank is continuous and uniformly distributed between 7 and 12 minutes. What is the probability that it takes Jolyn more than 11 minutes to wait? - ANS0.2 The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with a standard deviation of 2.4. I select a simple random sample of 15 plants of this variety and measure the time until maturity. The sample yields an average of 61.8 days. You read on the package of seeds that these tomatoes reach maturity, on average, in 60 days. You want to test to see if your seeds are reaching maturity later than expected. a. (4 points) State the hypotheses. You can use the HTML Editor to enter symbols including Greek letters. b. (4 points) If the p-value is 0.0018 and α=0.05, make a conclusion in a complete sentence related to the scenario. - ANSHo(Null): µ≤60 Ha(Alternative): µ>60 Due to alpha being greater than the p-value, the null hypothesis is rejected meaning that there is significant evidence proving that the seeds are reaching maturity later than expected. To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 25 students she meets walking on the campus late at night who are willing to give their opinion. Explain why the results cannot be trusted. - ANSThe results cannot be trusted because there is clear sampling bias present in the survey. The interview takes place at the campus late at night which is generally thought of as an unsafe setting, leading to the possibility that since people are out late at night they assume that their campus is safe since they are willing to walk around there during the time of night when there is less safety than during day. Additionally, this survey used convenience sampling which generally isn't as trusted as other types of sampling. Use the data from the previous question.(Image 1) Approximately what percentage of visitors spent more than 85 minutes at the museum that day? Round your answer to the nearest tenth of a percentage, and don't enter the % sign. - ANS5.7 Using the data from the previous question, what is the five-number summary? Enter the values from least to greatest. 5, 3, 7, 6, 6, 2, 5, 3, 4, 7 - ANS2, 3, 5, 6, 7 Using the data from the previous question(Image 4), what is P (X < 2)? - ANS0.268 Using the histogram from 4 questions earlier(Image 1), would it be better to use mean and standard deviation OR a five-number summary to describe this data? Briefly explain your reasoning. - ANSIt would be best to use a five-number summary because, there are outliers in this histogram which demerits the use of mean and standard deviation which rely on a lack of outliers. a five-number summary would be best used here since it includes median which can accurately find the center when there are outliers, additionally, using Q1 and Q3 you can find the IQR which can be used to accurately determine if there are outliers in play by cross-referencing that with the maximum and minimum, which is also shown in the five-number summary. Using the histogram from two questions earlier, describe the shape of the distribution.(Image 1) - ANSUnimodal and skewed right Using the table from 3 questions earlier(Image 4), answer the following. Given that a person is a current smoker, what is the probability that he/she is in very good health? Round to three decimal places. - ANS0.285 Using the table from 4 questions earlier(Image 4), answer the following. Given that a person is not a current smoker, what is the probability that he/she is in very good health? Round to three decimal places. - ANS0.399 Using the table from 5 questions earlier(Image 4), are health rating and smoking independent? Explain. - ANSHealth rating and smoking are not independent, but dependent. Due to the large number of nonsmokers having health exceeding good in contrast to the number of smokers predominately having health that is good or below it is safe to say that one's health is in fact dependent upon whether they smoke or not. This is further proven by the fact that since overall health of nonsmokers is significantly better than that of a smoker, smoking is bad for you and lowers the status of your health. Using the table from the previous question(Image 4), what is the probability that a randomly selected person is a current smoker? Round to 3 decimal places. - ANS0.094 Using the table from two questions earlier(Image 4), what is the probability that a randomly selected person is in poor health and not a current smoker? Round to 3 decimal places. - ANS0.003 Using your answer for the previous question, write the confidence interval in a complete sentence related to the scenario. (0.425, 0.476) - ANSWe are 95% confident that the proportion of U.S. adults who have never smoked a cigarette is between 0.425 and 0.476. Using your answer for the previous question, write the confidence interval in a complete sentence related to the scenario. (10.34, 12.46) - ANSWe can say with 95% confidence that the average amount of time a postal employee has worked for the postal service is between 10.34 years and 12.46 years. Using your answer for the previous question, write the confidence interval in a complete sentence related to the scenario. (96.66, 101.74) - ANSWe are 90% confident that this certain population on the WISC will have an average score between 99.66 and 101.74. Veterinarians often use nonsteroidal anti-inflammatory drugs (NSAIDs) to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating horses. They sent questionnaires to all the veterinarians on the list. Only 40% of them returned the questionnaire. Explain why the results cannot be trusted. (STUDY TYPES OF BIAS) - ANSThese survey results cannot be trusted because they contain voluntary bias meaning that people chose to fill them out and some didn't. Often times in these type of scenarios the majority of people filling out these surveys feel strongly about the issue whatever their stance may be. This leads to the population not accurately being represented since the people who don't care as much about the issue aren't surveyed since it heavily relies on volunteers. What is the approximate percentage of observations below the third quartile in a distribution? Hint: Think about the concept of quartiles. - ANS75