In Example 9.16, the sample size was n = 76, and we observed x̄ = 2.2 and s = 6.1.

We tested H0 : μ = 0 versus H1: μ > 0, and the P-value was 0.0012. Assume that the sample size was 41 instead of 76, but that the values of ̄x and s were the same.

a. Find the value of the test statistic t.

b. How many degrees of freedom are there?

c. Find the P-value.

d. Is the evidence against H0 stronger or weaker than the evidence from the sample of 76? Explain.

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Example 9.16 Perform a hypothesis test In a recent medical study, 76 subjects were placed on a low-fat diet. After 12 months, their sample mean weight loss was x = 2.2 kilograms, with a sample standard deviation of s = 6.1 kilograms. Can we conclude that the mean weight loss is greater than 0? Use the a = 0.05 level of significance.