In Exercise 5, the nonprofit consumer organization says that the standard deviation of the vehicle rating scores is 11.90. A random sample of 90 vehicle rating scores has a standard deviation of 11.96. At α = 0.10, is there enough evidence to reject the organization’s claim? Assume the population is normally distributed.

(a) Identify the claim and state H₀ and H_a.

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.

(c) Choose one of the options.

Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic.

Option 2: Find the appropriate standardized test statistic and the P-value.

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

Data from Exercises 5

A nonprofit consumer organization says that less than 18% of the vehicles the organization rated in a recent year have an overall score of 78 or more.
In a random sample of 90 vehicles the organization rated in a recent year, 20% have an overall score of 78 or more. At a = 0.05, can you support the organization’s claim?