Question

multiple choice 4 points
select the most appropriate response.
it is claimed that the mean age of bus drivers in chicago is 59.3 years. if a hypothesis test is performed, how should you interpret a decision
that fails to reject the null hypothesis?
there is not sufficient evidence to reject the claim μ = 59.3
there is sufficient evidence to reject the claim μ = 59.3
there is not sufficient evidence to support the claim μ = 59.3
there is sufficient evidence to support the claim μ = 59.3
multiple choice 4 points
select the most appropriate response

Explanation:

Step1: Understand hypothesis testing results

In hypothesis testing, when we fail to reject the null hypothesis ($H_0:\mu = 59.3$ in this case), it means we do not have enough evidence to say that the null hypothesis is false.

Step2: Analyze each option

• Option "There is not sufficient evidence to reject the claim $\mu=59.3$": This is incorrect. Failing to reject the null hypothesis is not the same as not having evidence to reject. The wording is off - we fail to reject, not that we lack evidence to reject in the way this option is phrased.
• Option "There is sufficient evidence to reject the claim $\mu = 59.3$": Since we failed to reject the null hypothesis, we do not have evidence to reject the claim about the mean.
• Option "There is not sufficient evidence to support the claim $\mu=59.3$": Failing to reject the null hypothesis does not mean we support the null hypothesis. We just do not have enough evidence to reject it.
• Option "There is sufficient evidence to support the claim $\mu = 59.3$": In hypothesis testing, we do not “support” the null hypothesis in the traditional sense. But when we fail to reject the null hypothesis ($H_0:\mu=59.3$), the most appropriate interpretation among the given options (even though the language is a bit non - standard in strict hypothesis testing terms) is that we do not have evidence to reject it, which is closest to the idea (in the context of these options) of having some (not in a strong evidentiary support way but in a lack of contrary evidence way) “sufficient evidence” (in the sense of not having contrary evidence) to support the claim (again, using the options' language) compared to the other options.

Answer:

There is sufficient evidence to support the claim $\mu = 59.3$