Use the data to identify the correct response.

Question

A simple random sample of 15-year old boys from one city is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population with a mean equal to 148 lb. Assume that the standard deviation of the weights of all 15-year old boys in the city is known to be 16.1 lb. Use the traditional method of testing hypotheses.

149 141 160 151 134 189 157 144 175 127 164

Choose the correct null and alternative hypotheses associated with this experiment.

A) H_0: μ ≠ 148 lb H_1: μ = 148 lb
B) H_0: μ ≥ 148 lb H_1: μ < 148 lb
C) H_0: μ = 148 lb H_1: μ ≠ 148 lb
D) H_0: μ ≤ 148 lb H_1: μ > 148 lb

Answer 1

To determine the correct null and alternative hypotheses for this experiment, we should start by analyzing the claim being tested. The claim is that the sample weights come from a population with a mean equal to 148 lb.

In hypothesis testing:

• The null hypothesis (H₀) usually represents a status quo or a statement of no effect, and in this case would assert that the population mean is equal to 148 lb.
• The alternative hypothesis (H₁) represents the opposite of the null and in this case would assert that the population mean is not equal to 148 lb.

Given this analysis, the correct null and alternative hypotheses are:

C) H₀: μ = 148 lb H₁: μ ≠ 148 lb