Question

a hospital spokesperson claims that the standard deviation of the waiting times experienced by patients in its minor emergency department is no more than 0.7 minutes. a random sample of 28 waiting times has a standard deviation of 0.8 minutes. at α = 0.10, is there enough evidence to reject the spokesperson’s claim? assume the population is normally distributed. complete parts (a) through (e) below. click the icon to view the chi - square distribution table. (some options for previous parts: a. fail to reject h₀. the standardized test statistic is in the rejection region. b. fail to reject h₀. the standardized test statistic is not in the rejection region. c. reject h₀. the standardized test statistic is not in the rejection region. d. reject h₀. the standardized test statistic is in the rejection region.) (e) interpret the decision in the context of the original claim. is there enough evidence to reject the spokesperson’s claim at the 10% level of significance? a. since the null hypothesis is not rejected, there is not enough evidence to reject the spokesperson’s claim. b. since the null hypothesis is rejected, there is enough evidence to reject the spokesperson’s claim. c. since the null hypothesis is rejected, there is not enough evidence to reject the spokesperson’s claim. d. since the null hypothesis is not rejected, there is enough evidence to reject the spokesperson’s claim.

Explanation:

In hypothesis testing, if we fail to reject the null hypothesis ($H_0$), it means the sample data does not provide sufficient evidence to contradict the null hypothesis (which in this case is related to the spokesperson's claim that the standard deviation is no more than 0.7 minutes). So, with the decision to fail to reject $H_0$, we conclude there's not enough evidence to reject the spokesperson's claim, matching option A.

Answer:

A. Since the null hypothesis is not rejected, there is not enough evidence to reject the spokesperson’s claim.