Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916
Assume that profits are normally distributed. Which of the following are appropriate hypotheses to test Becky's concern?

Question

Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are (in dollars) 1,743 1,438 1,212 1,705 1,985 1,857 1,916 Assume that profits are normally distributed. Which of the following are appropriate hypotheses to test Becky's concern? A) Η₀: σ² = 62,500, Η_A: σ² ≠ 62,500 B) Η₀: σ² < 62,500, Η_A: σ² ≥ 62,500 C) Η₀: σ² ≤ 62,500, Η_A: σ² > 62,500 D) Η₀: σ² ≥ 62,500, Η_A: σ² < 62,500

Quizplus · Accepted Answer

We want to test the null hypothesis that the standard deviation of profits for each week (σ) is less than or equal to $250. The alternative hypothesis will be that σ is greater than $250. Therefore, the appropriate choice is C because it has the correct direction of the alternative hypothesis. Choice A is incorrect because it has a two-tailed alternative hypothesis. Choice B is also incorrect because it has the wrong direction for the alternative hypothesis. Choice D is incorrect because it has a flipped direction for the alternative hypothesis.

Becky Owns a Diner and Is Concerned About Sustaining the Business