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A company that manufactures classroom chairs for high school students claims that the mean breaking strength of the chairs is 300 pounds. One of the chairs collapsed beneath a 220-pound student last week. You suspect that the manufacturer is exaggerating the breaking strength of the chairs, so you would like to perform a test of
H0: μ = 300
Ha: μ < 300
where μ is the true mean breaking strength of this company’s classroom chairs.
a. The power of the test to detect that μ = 294 based on a random sample of 30 chairs and a significance level of α = 0.05 is 0.71. Interpret this value.
b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).
c. Describe two ways to increase the power of the test in part (a).
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