Question

Suppose grade point averages are normally distributed. We are interested in whether smokers have different gpa’s than non-smokers. We know that non-smokers have a mean gpa of 3.1. You take a sample of 16 smokers and find they have a mean gpa of 3.38 with standard deviation of .021.

a. Suppose you wanted to test whether the gpas of the two groups different.

• write down the null and alternative hypotheses

• Construct the test statistic. What is the distribution of the test statistic?

• Is there evidence that the two groups differ ? (assume α = .1)

b. Suppose you wanted to test the hypothesis that smoker have higher gpa’s

• write down the null and alternative hypotheses

• Construct the test statistic. What is the distribution of the test statistic?

• Is there evidence that smokers have higher gpa’s (assume α = .05)

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 3.1
Alternative Hypothesis, Ha: μ ≠ 3.1

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (3.38 - 3.1)/(0.021/sqrt(16))
t = 53.333

P-value = 0
As P-value < 0.1, reject the null hypothesis.

Yes there is evidence

b)
Null Hypothesis, H0: μ = 3.1
Alternative Hypothesis, Ha: μ > 3.1

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (3.38 - 3.1)/(0.021/sqrt(16))
t = 53.333

P-value = 0
As P-value < 0.05, reject the null hypothesis.

there is evidence