Question

An advertisement for a popular weight loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. (You may find it useful to reference the appropriate table: z table or t table)

Set up the competing hypotheses to test the advertisement's claim.

A. μ₀: μ = 10; Hₐ: μ ≠ 10
B. μ₀: μ ≥ 10; Hₐ: μ < 10
C. μ₀: μ ≤ 10; Hₐ: μ > 10

Answer 1

To test the authenticity of the weight loss clinic's claim, we need to set up the competing hypotheses. Given that the advertisement suggests an average weight loss of more than 10 pounds, the null hypothesis (μ₀) would be that the mean weight loss is equal to 10 pounds, while the alternative hypothesis (Hₐ) would be that the mean weight loss is not equal to 10 pounds.

Step-by-step explanation:

To test the authenticity of the weight loss clinic's claim, we need to set up the competing hypotheses. Given that the advertisement suggests an average weight loss of more than 10 pounds, the null hypothesis (μ₀) would be that the mean weight loss is equal to 10 pounds, while the alternative hypothesis (Hₐ) would be that the mean weight loss is not equal to 10 pounds.

Therefore, the correct option would be A. μ₀: μ = 10; Hₐ: μ ≠ 10.