Your friend claims that he averages a 95% on his exams. You want to test his claim.

Question

Identify the null hypothesis.

Identify the alternative hypothesis.

A hypothesis test is conducted at the 7% significance level. If the p-value is 0.049, what conclusion should be drawn?
A. You cannot conclude that your friend doesn't average a 95% on his exams.
B. You conclude that your friend doesn't average a 95% on his exams.

Answer 1

To test your friend's claim that he averages a 95% on his exams, we set up the hypotheses as follows:

Null Hypothesis (H0):

The null hypothesis states that your friend's average is equal to 95%. \[ H_0: \mu = 95 \]

Alternative Hypothesis (H1):

The alternative hypothesis states that your friend's average is not equal to 95%. \[ H_1: \mu \neq 95 \]

This is a two-tailed test since we are interested in deviations from 95% in either direction.

Conclusion Based on P-value:

You are conducting the hypothesis test at the 7% significance level (α = 0.07) and you obtained a p-value of 0.049.

Since the p-value (0.049) is less than the significance level (0.07), you reject the null hypothesis.

Therefore, the conclusion that should be drawn is: B. You conclude that your friend doesn't average a 95% on his exams.