Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.001 . H o : μ = 66.5 H 1 : μ ≠ 66.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 72 with a mean of M = 62.5 and a standard deviation of S D = 13.5 . What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = ± What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 66.5. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 66.5. The sample data support the claim that the population mean is not equal to 66.5. There is not sufficient sample evidence to support the claim that the population mean is not equal to 66.5.

Answer 1

(a)

= 0.001

ndf = n - 1 = 72 -1 = 71

From Table, critical values of t = 3.433

(b)

SE = s/

= 13.5/ = 1.5910

Test statistic is:

t = (62.5 - 66.5)/1.5910 = - 2.514

So,

the test statistic is - 2.514

(c)

The test statistic is not in the critical region.

(d)

The test statistic leads to a decision to fail to reject the null.

(e) As such the final conclusion is that there is not sufficient evidence to support the claim that the population mean is not equal to 66.5.