The annual salaries (in dollars) of 14 randomly chosen fire fighters are listed.

Question

The annual salaries (in dollars) of 14 randomly chosen fire fighters are listed. At = 0.05, is there enough evidence to support the claim that the standard deviation of the annual salaries is different from $5650? Assume the population is normally distributed. Complete parts (a) through (e) below.

51,040

37,849

A) write the claim mathmatically and identify Ho and Ha

B) find the critical value(s)

²o= ______

(round to three decimal places as needed. Use comma to separate answers as needed.)

C) find the standarized test statistic for the ² test

²= ___________

D) decide whether to reject or fail to reject the null hypothesis.

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 the fire fighters is different from $5650 at the 5% level of significance?

50,724 40,990 52,403 46,484 41,753 40,207

51,040

52,017 43,846 34,865 35,002 28,284 32,788

37,849

Explanation / Answer

Ho : = 5650

H1 : 5650

From the alternate hypothesis, it is a two tailed test at 5% level of significance.

Therefore, the critical value is 2(/2, n-1) = 2(0.025, 13) = 24.74 ( from chi-square table)

The test statistic:

2cal = (n-1)( s/5650)2

s = [(x - x)2 / n-1 = [60330645/13] = 7767.281

2 = 13*(7767.281/5650)2 = 24.56

Since 2cal (24.56) < 2(0.025, 13) (24.74), we fail to reject the null hypothesis, and hence conclude that = 5650.

There is no evidence to support the claim that the standard deviation of annual salaries of the fire fighters is different from $5650 at the 5% level of significance.

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