Question

Consider the following statement: “If a test statistic has a standard normal distribution (assuming that H0 is true) and the significance level is 0.05, then the critical values in a two-sided test are -1.64 and +1.64.”

Indicate whether you agree or disagree with the statement and explain your answer.

Part (b) Consider the following statement: “If a university claims that the mean starting salary of their graduates is $47,000 or more and you find that the mean starting salary in a sample of 45 recent graduates is $45,880, then we have proof that the university’s claim is false.” Indicate whether you agree or disagree with the statement and explain your answer.

Part (c) Consider the following statement: “The smallest possible p-value is negative infinity.” Indicate whether you agree or disagree with the statement and explain your answer.

Answer 1

(a)

For two-sided test, the significance level becomes 0.05/2 = 0.025. The critical values at p = 0.025 and 1 - 0.025 = 0.975 for standard normal distribution is -1.96 and +1.96. Hence we disagree with the given statement.

(b)

H0: Mean salary $47,000

H1: Mean salary < $47,000

Let s be the standard deviation of mean starting salary of their graduates. Then for significance level of 0.05, the critical value of mean salary below which we reject the claim (reject H0) is 47,000 - 1.96 s.

If s is such that 47,000 - 1.96 s > 45,880, then we cannot reject the claim (reject H0.

So, it depends on the standard deviation of mean starting salary of their graduates. It can be possible that the standard deviation of mean starting salary is such that we cannot reject the claim. So, we disagree with the statement.

(c)

The p-value is the probability of finding the observed, or more extreme, results when the null hypothesis (H0) of a study question is true. Since the probability value cannot be negative and lies between 0 and 1, the smallest possible p-value is 0. So, we disagree with the statement.