Previous Exam 3 (Spring 2023) (3)

Use the following to answer questions 1 - 6: A distribution company wants to estimate the mean weight of fully loaded trucks that leave from their distribution center. A random sample of 16 trucks was taken and the sample mean was found to be 42,500 pounds with a sample standard deviation of 1,000 pounds. Create a 95% confidence interval estimate for the population mean weight of fully loaded trucks that leave from the distribution center. (Assume all necessary assumptions are satisfied.) 1. Give the point estimate (Do not round the number). 2. Give the critical value (Do not round the number) 3. Give the standard error (Do not round the number) 4. State the margin of error. (Do not round the number) 5. Calculate the confidence interval. (Do not round the number). 6. Interpret the interval you calculated in the previous question as we have done in lecture.

Use the following to answer questions 7-11 : A distribution company works with different shaped packages but the company prefers square boxes because they stack in the trucks better. The company states that more than 85% of packages are square shaped. A random sample of 100 boxes was taken and 87 were square shaped. Is there sufficient evidence the population proportion of boxes that are square shaped is more than 85%? Use a level of significance of 0.05. 7. State the correct hypotheses (using the notation covered in lecture). H 0 : H a : 8. Calculate the appropriate test statistic (round to two decimal places) 9. Calculate the appropriate p-value (round to four decimal places) 10. State your decision. (circle one) Accept H 0 Reject H 0 Do Not Reject H 0 11. Interpret the results in the way we did in lecture.

Use the following to answer questions 24 – 28 : There has been a debate recently that employees who work a four-day work week are more productive than those that work a five-day work week. A distribution center decides to test this. A random sample of 20 workers was taken. The number of boxes packaged was calculated during a four-day work week and then the number of boxes packaged was calculated during a five-day work week. (Note it was the same 20 workers used for both values provided). The following output was generated to determine the following:  Note: o μ 1 = populationmeannumber of boxes packaged during four − day work week . o μ 2 = populationmean numberof boxes packaged during five − day work week . o Level of significance = 0.05  Hypothesis test was performed to determine if the population mean number of boxes packaged during a four- day work week is greater than the population mean number of boxes packed during of a five-day work week. o H 0 : μ d = 0 vs. H 0 : μ d > 0 where μ d = μ 1 − μ 2 o T-Statistic = 3.39 o P-value = 0.0015  95% confidence interval estimate for the difference between the population means. o Estimate for μ 1 − μ 2 o Confidence Interval = (1.13, 4.77). 24. Are the two samples described dependent or independent? Dependent Independent 25. Which test should be performed based on your answer to the previous question? Note you answer here must match your answer to the previous question. Paired t – test Two sample t-test 26. Based on the output given from Excel, what is the correct decision for the hypothesis test? a. Reject H 0 b. Do Not Reject H 0 c. Accept H 0 27. Based on the given confidence interval, is there evidence of a difference between the two population means? a. There is evidence of a difference because the confidence interval contains zero. b. There is not evidence of a difference because the confidence interval contains zero. c. There is evidence of a difference because the confidence interval does not contain zero. d. There is not evidence of a difference because the confidence interval does not contain zero. 28. Based on the given confidence interval, which population mean is greater? a. μ 1 = populationmeannumber of boxes packaged during four − day work week . b. μ 2 = populationmean number of boxes packaged during five − day work week . c. We can’t make the statement that either mean is greater because it is possible they are the same.