You wish to test the following claim (H_a) at a significance level of alpha = 0.

Question

You wish to test the following claim (H_a) at a significance level of alpha = 0.10. H_0: mu = 68.7 H_a: mu notequalto 68.7 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = plusminus 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 68.7. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 68.7. The sample data support the claim that the population mean is not equal to 68.7. There is not sufficient sample evidence to support the claim that the population mean is not equal to 68.7.

Explanation / Answer

critical value at 0.1 level of significance and 14 degree of freedom =-/+ 1.761

test statistic =-1.107

test statistic is not in critical region

test statsitic leads to a decision to fail to reject the null

final conclusion is that

there is not sufficient evidence to support the claim that the population mean is not equal to 68.7.

X 55.7 53.9 69.7 65.1 54.8 71.2 58.8 89.2 68.2 62.8 68.8 59.5 69.2 76.3 67.7 mean(X) 66.060 std deviation(S) 9.235 std error =S/(n)1/2 2.384 t=(X-68.7)/std error -1.107

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