6.118 Planning another test to compare consumption. Example 6.15 (page 372) gives a test of a hypothesis about the mean consumption of sugar-sweetened beverages at your university based on a sample of size n = 100. The hypotheses are

H₀: μ = 286
H_a: μ ≠ 286

While the result was not statistically significant, it did provide some evidence that the mean was smaller than 286. Thus, you plan to recruit another sample of students from your university, but this time use a one-sided alternative. You were thinking of surveying n = 100 students but now wonder if this sample size gives adequate power to detect a decrease of 15 calories per day to μ = 271.

1. (a) Given α = 0.05, for what values of z will you reject the null hypothesis?

2. (b) Using σ = 155 and μ = 286, for what values of will you reject H₀?

3. (c) Using σ = 155 and μ = 271, what is the probability that will fall in the region defined in part (b)?

4. (d) Will a sample size of n = 100 give you adequate power? Or do you need to find ways to increase the power? Explain your answer.

5. (e) Use the Statistical Power applet or other statistical software to determine the sample size n that gives you power near 0.80.