When 10 randomly selected car owners are surveyed, it is found that the mean length of time they plan to keep their car is 7.01 years, and the standard deviation is 0.74 years. Assume that times are normally distributed.
-The null and alternative hypotheses to test the claim that the mean for all car owners is less than 7.5 years is _____.

Question

When 10 randomly selected car owners are surveyed, it is found that the mean length of time they plan to keep their car is 7.01 years, and the standard deviation is 0.74 years. Assume that times are normally distributed. -The null and alternative hypotheses to test the claim that the mean for all car owners is less than 7.5 years is _____. A)H₀: ? = 7.5 vs.H_a: ? ? 7.5 B)H₀: ? ? 7.5 vs.H_a: ? < 7.5 C)H₀: ? ? 7.01 vs.H_a: ? < 7.01 D)H₀: ? ? 7.5 vs.H_a: ? = 7.5 E)H₀: ? ? 7.5 vs.H_a: ? > 7.5

Quizplus · Accepted Answer

The null hypothesis (H0) always includes the equality condition, and since we are testing the claim that the mean is less than 7.5 years, the alternative hypothesis (Ha) should reflect this claim. Therefore, H0: μ ≥ 7.5 vs. Ha: μ < 7.5 is the correct formulation.

When 10 Randomly Selected Car Owners Are Surveyed, It Is