Question

the annual salaries (in dollars) of 14 randomly chosen fire fighters are listed. at α = 0.05, is there enough evidence to support the claim that the standard deviation of the annual salaries is different from $5350? assume the population is normally distributed. complete parts (a) through (e) below. 50,762 40,962 52,386 46,539 41,734 40,173 51,138 52,013 43,827 34,908 35,096 28,222 32,693 37,832 click the icon to view the chi - square distribution table. b. fail to reject h₀. the standardized test statistic is in the rejection region. c. reject h₀. the standardized test statistic is in the rejection region. d. fail to reject h₀. the standardized test statistic is not in the rejection region. (e) interpret the decision in the context of the original claim. is there enough evidence to support the claim that the standard deviation of the annual salaries of fire fighters is different from $5350 at the 5% level of significance? a. since the null hypothesis is not rejected, there is enough evidence to support the claim. b. since the null hypothesis is rejected, there is not enough evidence to support the claim. c. since the null hypothesis is not rejected, there is not enough evidence to support the claim. d. since the null hypothesis is rejected, there is enough evidence to support the claim.

Explanation:

In hypothesis testing, if we reject the null hypothesis ($H_0$), it means the sample data provides sufficient evidence to support the alternative claim (here, that the standard deviation of firefighters' annual salaries is different from $5350$) at the given significance level ($\alpha = 0.05$). Option D correctly links the rejection of $H_0$ to having enough evidence for the claim.

Answer:

D. Since the null hypothesis is rejected, there is enough evidence to support the claim.