Math 120 Statistics Week 10 Worksheet Hypothesis Tests for the Mean You are expected to use correct mathematical notation for all assignments. That includes using accurate symbols for Greek letters (like u, o, and a) and correct symbols for inequalities (, #). If you do not know how to do this, use the videos posted on Canvas under the Start Here module. Write the null and alternative hypothesis for each situation. 1. A report from several decades ago states that the mean height of a first grader in the U.S. is 30 inches. We want to test to determine if the mean height has changed. 2. A report states that the mean credit card debt for college students in the U.S. is $1,185. A college administrator thinks the mean credit card dept at her college would be lower than this. 3. A certain manufacturing company believes it is ideal if at most 20% of customer service calls last less than 10 minutes. We want to test to see if more than 20% of customer service calls last more than 10 minutes. Write a sentence to interpret the decision made in each example. 4. Assume that, in problem 1 above, we decide to reject Ho. Interpret this decision. 5. Assume that, in problem 2 above, we fail to reject Ho. Interpret this decision.In each case, interpret what a type I and type II error would mean in the context of the problem. 6. Write a sentence to interpret the meaning of a type I error in problem 1 above. 7. Write a sentence to interpret the meaning of a type II error in problem 2 above. Given each p-value, determine if the null hypothesis Ho should be rejected at the 5% significance level a = 0.05. 8. p= 0.126 9. p= 0.0054You may use calculator tests to find the test statistic and p-value. Show what test you used and write what you typed in your calculator test to get your answer. Include all five steps of a hypothesis test: State the null and alternative hypothesis State the test statistic State the p-value Decide whether Ho should be rejected Write a sentence to interpret your results. 1. In the United States, it is well-known that for the population of males, the mean height is 69.1 inches with standard deviation 4 inches. A researcher claims that the mean height of a certain group of males is significantly different that this, due to genetic factors. For a sample of 20 such men, the data is given: 67.0 68.5 69.0 64.5 71.0 70.5 64.5 72.0 76.5 62.0 78.0 75.5 74.0 67.5 72.0 71.5 68 72.5 64.0 73.5 Assume the population is normally distributed. Test the researcher's claim. At significance level 1% (a = 0.01), what can be concluded? 2. A report states that the mean age of all college students in the United States is 26.4 years. An administrator thinks the mean age for students at her college is higher than the national average. She randomly surveys 50 students at her college and finds that the sample mean is 28.6 years with a standard deviation of 5.1 years. At the 5% level of significance (a = 0.05), what can be concluded?3. A survey in the New York Times Almanac finds the mean commute time to work (one way) for is 25.4 minutes for the fifteen largest cities in the U.S. A researcher believes that, due to work-from home policies during the pandemic, this value is now lower than 25.4 minutes. After collecting a sample of 100 people in these cities, he finds the mean commute is 22.1 minutes with standard deviation 6.8 minutes. a. At the a = 0.05 level of significance, what can be concluded? b. Your classmate asks, "Didn't he already find that the mean commute was less than 25.4 minutes? He found 22.1 minutes in his sample. Doesn't that prove the mean is smaller than 25.4 minutes? Why do we need the hypothesis test?" In other words, explain the purpose of a hypothesis test to your classmate. Explain in your own words