Question

1. One student was upset with her grade on Test 2 and thought the test was too difficult. In her anger, she said, "There is no way the class average on this test was higher than a C." Can you conclude at a 0.05 level of significance that the average score on Test 2 was no higher than a 79?

Answer 1

Hypothesis rejected

Explanation:

Lets use the t-test since the variance of the population is now known. We need to test the hypothesis that H_0: \mu \leq 79 \text{ vs } H_1: \mu > 79 . This is performed in R as follows:

t.test(tt$Test.2.Score,mu=79,alternative="greater")

One Sample t-test

data: tt$Test.2.Score

t = 2.9238, df = 69, p-value = 0.002337

alternative hypothesis: true mean is greater than 79

95 percent confidence interval:

81.26555 Inf

sample estimates:

mean of x

84.27143

Thus, we reject the null hypothesis and conclude that \mu > 79.