The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: A) H₀: μ ≥ 30 versus H₁: μ 30. C) H₀: X ≥ 30 versus H₁: X 30.

Question

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: A) H₀: μ ≥ 30 versus H₁: μ < 30. B) H₀: μ ≤ 30 versus H₁: μ > 30. C) H₀: X ≥ 30 versus H₁: X < 30. D) H₀: X ≤ 30 versus H₁: X > 30.

Quizplus · Accepted Answer

The null hypothesis (H₀) should always assume no effect, in this case that the mean age is less than or equal to 30. The alternative hypothesis (H₁) should assume an effect in the direction of interest, in this case that the mean age is greater than 30. Therefore, the appropriate hypotheses to test are H₀: μ ≤ 30 (no effect) versus H₁: μ > 30 (effect in the direction of interest). Choice B is the only option that matches this format.

The Owner of a Local Nightclub Has Recently Surveyed a Random