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Answer the following questions showing all work.  Full credit will not be given to answers without work shown. If you use Minitab Express or StatKey include the appropriate output (copy + paste). If you do hand calculations show your work using the Word equation editor. Clearly identify your final answers. Output without explanation will not receive full credit and answers with no output or explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

1. Fill in the table below with the assumptions that must be met in order to estimate each sampling distribution with a z or t distribution.  The first row is completed as an example. [10 points]

2. A random sample of STAT 200 students were surveyed and asked to name their favorite beverage. Of the 50 participants, 34 preferred a non-alcoholic beverage and 16 preferred an alcoholic beverage. Is there evidence that in the population of all STAT 200 students more than 50% prefer a non-alcoholic beverage? Use Minitab Express and the five-step hypothesis testing procedure.   [20 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide between the null and alternative hypotheses

Step 5: State a “real world” conclusion

3. For this question set you will be using the Spring17.MTW dataset.  Assume that these data are representative of the population of all World Campus STAT 200 students.  We want to know if people who are and are not currently dieting differ in terms of their weights [25 points].

A. Create a graph that displays the distributions of weights for students who are and are not currently dieting.

B. Use the five step hypothesis testing procedure to determine if there is evidence that students who are and are not currently dieting differ in terms of their weights.

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide between the null and alternative hypotheses

Step 5: State a “real world” conclusion

4. Use the dataset Spring17Data.MTW to answer the following questions using Minitab Express. Assume that these data are representative of the population of all Penn State World Campus STAT 200 students. [25 points]

A. Construct a dotplot of the variable Hours Per Week Watching TV.

B. Describe the shape of your dotplot in part A.

C. Explain how and why the Central Limit Theorem can be applied to the variable of Hours Per Week Watching TV.

D. Construct a 95% confidence interval for the mean hours per week spent watching TV in the population of all Penn State World Campus STAT 200 students. Use the method covered in the online notes this week that estimates the sampling distribution with the t distribution.

E.  Interpret the confidence interval that you constructed in part D.

F. If you wanted to estimate the mean hours per week spent watching TV in the population of all Penn State World Campus STAT 200 students with a margin of error of 0.25 hours what minimum sample size should you obtain?

5. I want to compare the midterm exam and final exam scores from a sample of online STAT 200 students from the Summer 2016 semester.  In a random sample of 30 students the mean midterm exam score was 83.037 with a standard deviation of 15.155. The mean final exam score was 77.133 with a standard deviation of 13.480. The mean difference in scores (midterm – final) was 5.903 with a standard deviation of 15.049. Use the five-step hypothesis testing procedure to determine if there is evidence that the scores on the midterm exam and final exam are different in the population of all online STAT 200 students. [20 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide between the null and alternative hypotheses

Step 5: State a “real world” conclusion

Extra Credit (6 points max)

In the population, SAT-Math scores are normally distributed with a mean of 500 and standard deviation of 100. Use Minitab Express to answer each of the following questions.

A. If you were to randomly select one test taker, what is the probability that he or she would have score 600 or higher?

B. If you were to take a random sample of n=10 test takers, what is the probability that their sample mean would be 600 or higher? Use Minitab Express and the five-step hypothesis testing procedure.  

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide between the null and alternative hypotheses

Step 5: State a “real world” conclusion

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