Hypothesis Testing Worksheet

1) Each of the following situations requires a significance test about a population mean State the appropriate null hypothesis H0 and alternative hypothesis Ha in each case:

• Census Bureau data shows that the mean household income in the area served by a shopping mall is $8,500 per year. A market research firm questions shoppers at the mall to find out whether the mean household income of mall shoppers is higher than that of the general population.

• Last year, your company's service technicians took an average of 2.8 hours to respond to trouble calls from business customers who had purchased service contracts. Do this year's data show a different average response time?

2) The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200, with 200 being the highest level of motivation. The mean score for U.S. college students is about 125, and the standard deviation is about 35. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 20 students who are at least 30 years of age. The teacher now collects the data from the 20 students, and their mean is 135.2. Is this evidence of a significantly higher score by older students?

3) Your company sells exercise clothing and equipment on the Internet. To design the clothing, you collect data on the physical characteristics of your different types of customers. We take a sample of 25 male runners and find their mean weight to be 62.88 kilograms. Assume that the population standard deviation is = 5.5.

• Calculate a 95% confidence interval for the mean weight of all such runners

• Based on this confidence interval, does a test of

H0: = 62.88 kg

HA: 62.88 kg

reject H0 at the 5% significance level?

• Carry out the hypothesis test in 3 to verify your answer:

4) Last year the government made a claim that the average income of the American people was $22,950. However, a sample of 50 people taken recently showed an average income of $24,090 with a population standard deviation of $300. Is the government's estimate too low? Conduct a significance test to see if the true mean is more than the reported average. Use an alpha = 0.01.