1. Test the claim that the mean GPA of night students is smaller than 2.9 at the .025 significance level. The null and alternative hypothesis would be:

• H0:p=0.725H0:p=0.725 H1:p<0.725H1:p<0.725
• H0:=2.9H0:=2.9 H1:2.9H1:2.9
• H0:=2.9H0:=2.9 H1:<2.9H1:<2.9
• H0:p=0.725H0:p=0.725 H1:p0.725H1:p0.725
• H0:=2.9H0:=2.9 H1:>2.9H1:>2.9
• H0:p=0.725H0:p=0.725 H1:p>0.725H1:p>0.725

Based on a sample of 80 people, the sample mean GPA was 2.85 with a standard deviation of 0.08 The test statistic is (to 3 decimals) The critical value is (to 3 decimals) Based on this we

• reject the null hypothesis
• fail to reject the null hypothesis

2. A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was less than 9 years. A survey of 92 companies reported in The Wall Street Journal found a sample mean tenure of 8.5 years for CEOs with a standard deviation of 5.7 years (The Wall Street Journal, January 2, 2007). You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of 0.001. Your hypotheses are: H0:9H0:9 H1:<9H1:<9 What is the test statistic for this sample? (Report answer accurate to 3 decimal places.) What is the p-value for this sample? (Report answer accurate to 4 decimal places.) This test statistic leads to a decision to

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that

• there is sufficient evidence to conclude that the population mean tenure for CEOs is equal to 9.
• there is not sufficient evidence to conclude that the population mean tenure for CEOs is equal to 9.
• there is sufficient evidence to conclude that the population mean tenure for CEOs is less than 9.
• there is not sufficient evidence to conclude that the population mean tenure for CEOs is less than 9.

3. It's proposed that the average life expectancy these days is 71.1, but recent data suggests it might be less than that. A sample size of 74 countries found a sample mean life expectancy of 61.6 years with a standard deviation of 20.5 years. You want to formulate and test a hypothesis that can be used to challenge the validity of the claim at a significance level of 0.001. With hypotheses H0:71.1H0:71.1 vs H1:<71.1H1:<71.1, what is/are the critical value(s)? (Report answer accurate to 2 decimal places.) What is the test statistic for this sample? (Report answer accurate to 3 decimal places.) What is the p-value for this sample? (Report answer accurate to 4 decimal places.) Our decision is to

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that

• there is sufficient evidence to conclude that the population mean life expectancy is equal to 71.1.
• there is not sufficient evidence to conclude that the population mean life expectancy is equal to 71.1.
• there is sufficient evidence to conclude that the population mean life expectancy is less than 71.1.
• there is not sufficient evidence to conclude that the population mean life expectancy is less than 71.1.