Previous Final Exam A

Name: Final Exam A: STAT 201 Murphy Directions: Answer each question to the best of your ability. Round to two decimal places, at least. Make sure you provide appropriate interpretations when they are asked for. The points allowance for each part of a question is provided. There are a total of 120 points on this exam. Good luck. 1. A study was done that analyzed the number of final exams that are offered as take home test for freshmen at USC who are taking 5 course this semester. The population mean number of take home exams was known to be 1.5 exams. A sample of 1,000 USC freshmen was taken and it was determined that the mean number of take home exams was 1.23 exams. a. Identify the population in this description. (2 points) b. Identify whether the mean of 1.23 exams is a parameter or statistic. (2 points) Circle choice below. Parameter Statistic c. Identify if the variable of interest (the number of take home exams) is categorical, discrete quantitative, or continuous quantitative. (2 points) Circle choice below. Categorical Discrete Quantitative Continuous Quantitative d. Identify two types of graphs that can be used to provide a visual for this dataset. (note that your answer should correspond to your answer for part c). (2 points) 2. Students are often in a hurry to grab something to eat for lunch in the Russell house between classes. A random sample of 18 students was taken during the busiest time at the Russell house (12 pm to 1 pm) and the amount of time each student waited to get food and pay was recorded. The following are the 18 different observations: 2 3 3.5 4 4 4.5 5 5 5.5 6 6 6 6.5 7 7.5 8 8.5 9 Note: ∑ ࠵? = 101 and ∑(࠵? − ࠵?̅) ! = 63.78 a. Calculate the sample mean wait time. (2 points) b. Calculate the sample standard deviation of the wait times. (2 points) c. Calculate the five number summary for wait times. (6 points)

3. The following results provide information about the difference between the number of days of class missed between an introductory level statistics class that used attendance as part of the final grade and an introductory level statistics class that does not use attendance as part of the final grade. Dataset Sample size (n) Mean Standard Deviation Range Interquartile Range Minimum First Quartile Second Quartile (Median) Third Quartile Maximum Attendance is Part of the Final Grade 22 0.91 1.02 3 **** 0 0 1 2 3 Attendance is Not Part of the Final Grade 25 **** 2.49 9 3 0 1 **** 4 9 a. State two measurements that are resistant. (2 points) b. Which dataset appears to have more variability in the number of days missed? (2 points) Circle One below. Dataset where attendance is part of the final grade. Dataset where attendance is not part of final grade. c. Based on the statistics and/or boxplot is there reason to believe that the attendance policy has an effect on the number of classes missed. Justify your answer by referencing a statistic and/or the boxplot. (2 points) d. What is the shape of the dataset based on the boxplot for the dataset Attendance Not Part of Grade (the bottom boxplot)? (2 points) Normal (bell-shaped) Right-skewed Left-skewed e. Based on your answer to part d, which of the following is the correct relationship between the mean and the median? Your answer must agree with what you put as the answer to part d. (2 points) Mean ≈ Median Mean < Median Mean > Median f. Calculate the Interquartile range for the dataset “Attendance is Part of Grade”. (2 points) g. What is the balance point of the dataset where attendance is part of the grade? (2 points) h. What is the average distance an observation falls from the mean of the dataset where attendance is part of the grade? (2 points) i. What is the value at which 75% of the data falls below for the dataset where attendance is part of the grade? (2 points)

5. Assume that the population mean ATM withdrawal is known to be $60 with a population standard deviation of $35. Also assume that it is known that the data follows a normal distribution. a. Find and interpret the z-score of an ATM withdrawal of $20. (4 points). b. What is the probability of an ATM withdrawal of more than $100? (3 points) 6. A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 25 nonprofits, the sample mean one-time gift donation in the past year was $75, with a sample standard deviation of $9. Construct and interpret a 95% confidence interval estimate for the population mean one- time gift donation. You must provide answers for each step below to get full credit. a. State the point estimate used in the calculation of the confidence interval. (1 point) b. Calculate the standard error used in the calculation of the confidence interval. (2 points) c. State the critical value used in the calculation of the confidence interval. (2 points) d. State the margin of error used in the calculation of the confidence interval. (1 point) e. Provide the 95% confidence interval. (1 point) f. State two ways you can make the interval wider. (Circle one choice for both of the following) (2 points) i. How would you change the sample size? Increase n Decrease n ii. How would you change the level of confidence? Increase Confidence Level Decrease Confidence Level g. What would your decision be for a hypothesis test using a level of significance of 0.05 if we wanted to know if there was evidence that the population mean was greater than $70? Hint: use your confidence interval to answer the question. (circle one choice) (1 point) Reject ࠵? " Do Not Reject ࠵? "

7. The US Department of Education reports that 40% of full-time college students are employed while attending college. A recent survey of 60 full-time students at a university found that 30 were employed. Is there evidence, using a 0.05 level of significance, to determine whether the proportion of full-time students at the university that are employed is different from the national norm of 0.40? a. What is the probability of getting a Type I error? (2 points) b. State the hypothesis. (2 points) c. Calculate the appropriate test statistic. (2 points) d. Calculate the p-value. (3 points) e. State your decision. (2 points) f. Interpret the results in the context of the problem. (2 points)

9. Some researchers claim that music can be relaxing and reduce stress. Assume that stress is measured by pulse rate (a higher pulse rate indicates stress while a lower pulse rate indicates a more relaxed state). Twelve patients that suffer from job related stress were randomly sampled and the following measurements were taken: initial pulse rate and pulse rate after participating in a month long music-listening, relaxation-therapy program. Assume that the underlying distributions of initial and final pulse rates are normally distributed and use a level of significance of 0.05. The researchers are trying to determine if there is evidence that there is a difference in the pulse rate between the mean initial pulse rate and the mean pulse rate after the music-listening, relaxation-therapy program? Use this information and the following StatCrunch output to answer the questions that follow. Hypothesis test results: Difference Mean Std. Err. DF T-Stat P-value Initial Pulse Rate - Final Pulse Rate 6.3333333 2.520622 11 2.5126073 0.0289 95% confidence interval results: Difference Mean Std. Err. DF L. Limit U. Limit Initial Pulse Rate - Final Pulse Rate 6.3333333 2.520622 11 0.7854817 11.881185 a. Are the samples independent or dependent? (Circle one). (2 points) Independent Dependent b. Which is the statistic used in the confidence interval and test statistic calculations? (Circle one). (2 points) ࠵? ̅ ࠵?̅ # − ࠵?̅ ! ࠵? # − ࠵? ! c. Which of the following tests should be performed? (Circle one). (2 points) Two-sample t-test. Paired t-test. d. State the hypothesis used to test this claim. (2 points) e. State the decision of the hypothesis test. (2 points) f. Based on the Confidence Interval which pulse rate was higher. (Circle One). (2 points) Initial Pulse Rate Final Pulse Rate Neither was always higher. g. Based on the confidence interval is it possible that there is a difference in the mean pulse rate before and after the therapy. Justify your answer. (2 points)

10. According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 13.6 and a standard deviation of 3.0. a. Find the mean of the sampling distribution of the sample means, if the sample size is 36. (2 points) b. Find the standard deviation of the sampling distribution of the sample means, if the sample size is 36. (2 points) c. State the effect of increasing the sample size on both the mean and standard error of the sampling distribution: i. The mean will if the sample size is increased. (2 points) decrease increase stay the same ii. The standard error will if the sample size is increased. (2 points) decrease increase stay the same d. Would a sample mean of 15 be considered unusual for a sample of size 36? Justify your answer. (2 points) After you complete your exam, please sign the statement below, taken from the Office of Academic Integrity: I understand that it is the responsibility of every member of the Carolina community to uphold and maintain the University of South Carolina’s Honor Code. As a Carolinian, I certify that I have neither given nor received unauthorized aid on this exam. Sign ______________________________________________