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What minimum sample size would be necessary to construct a 95% confidence interval for the mean difference in exam scores with a margin of error of 0.5 points?

1. A STAT 200 instructor wants to know if students tend to score differently on the first and second midterm exams. Data were collected from a representative sample of 80 students during the Spring 2018 semester. Data were paired by student. The mean difference, computed as Midterm 1 – Midterm 2, was 5.2076 points with a standard deviation of 5.8854 points. [60 points]

A. Explain why it is appropriate to use the t distribution to approximate the sampling distribution in this scenario.

B. Use Minitab Express to conduct a paired means t test to determine if there is evidence that scores on the two exams are different in the population of all STAT 200 students. Use the five-step hypothesis testing procedure given below. Remember to include all relevant Minitab Express output. Do not do any hand calculations.

C. use Minitab Express to conduct a single sample mean t test given a sample size of 80, sample mean of 5.2076, and sample standard deviation of 5.8854 to determine if there is evidence that the population mean is different from 0. Use the five-step hypothesis testing procedure given below. Remember to include all relevant Minitab Express output. Do not do any hand calculations.

D. Explain why your test statistic and p value were the same in parts B and C.

E. What minimum sample size would be necessary to construct a 95% confidence interval for the mean difference in exam scores with a margin of error of 0.5 points? You will need to do hand calculations. Show all of your work.

2. Data concerning employment status were collected from a sample of 100 World Campus students at the beginning of the Fall 2018 semester. In that sample of 100, 67 were employed full-time. [40 points]

A. We want use these data to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time. Is it appropriate to use the normal approximation method? Show how you checked assumptions.

B. Use Minitab Express to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time. If assumptions were met in part A, use the normal approximation method. Remember to include all relevant Minitab Express output and to clearly identify your answer. Do not do any hand calculations.

C. What sample size would be necessary to construct a 95% confidence interval to estimate the proportion of all World Campus students who are employed full-time with a margin of error of 5%? You will need to do hand calculations. Show all of your work.

D. We want to know if there is evidence that in the population of all World Campus students, more than 60% are employed full-time. Use Minitab Express and the five-step hypothesis testing procedure given below. Remember to include all relevant Minitab Express output. Do not do any hand calculations.