1. Ch. 17/7 – You conduct a survey of a sample of 25 members of this year’s graduating marketing students and find that the average GPA is 3.2. The standard deviation of the sample is 0.4. Over the last 10 years, the average GPA has been 3.0. Is the GPA of this year’s students significantly different from the long-run average? At what alpha level would it be significant?
Null hypothesis H0: µ=3.0
Alternative hypothesis H1: µ≠3.0
Given the sample mean xbar=3.2, sample standard deviation s=0.4 and sample size n=25. We can use t-test.
The test statistic can be computed as follows:
T=(xbar-3.0)/s*sqrt(n)
=(3.2-3.0)/0.4*sqrt(25)
=0.2/0.4*5=2.5
Note that the degree of freedom df=25-1=24. So, we can get p-value=P(T>2.5)
=0.0197
So, if we use significance level alpha = 0.02, then since p-value=0.0197<alpha=0.02, we should reject Null hypothesis H0.
Hence, at a 0.02 significance level, we conclude that the GPA of this year’s students is significantly different from the long-run average.

2. Ch. 17/9 – You contact a random sample of 36 graduates of Western University and learn that their starting salaries averaged $28,000 last year. You then contact a random sample of 40 graduates from Eastern University and find that their average starting salary was $28,800. In each case, the standard deviation of the sample was $1,000. a. Test the null hypothesis that there is no difference between average salaries received by the graduates of the two schools.
TO determine if there is a significant difference between the average salaries received by graduates of the two schools; you would use the null hypothesis and the alternative hypothesis, which forms the basis for a test of hypothesis inference. The alternative hypothesis will take the form of a two tailed test with alpha = 0.05. This means that we are 95% confident that we will make the correct inference