Question

You wish to test the following claim (Ha) at a significance level of α-0.001 You believe both populations are normally distributed, but you do not know the standard deviations for either However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n,-26 with a mean of M, 69.3 and a standard deviation of SD,-10.8 from the first population. You obtain a sample of size n2 11 with a mean of M2 64.3 and a standard deviation of SD2-19.8 from the second population. What is the critical value for this test? For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (Report answer accurate to three decimal places.) critical value =士 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic- The test statistic is... O in the critical region O 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 first population mean is not equal to the second population mean. There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean. The sample data support the claim that the first population mean is not equal to the second population mean. There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

Answer 1

Test Statistic :-

t = 0.995

Test Criteria :-
Reject null hypothesis if

Critical value  

Result :- Fail to Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 0.9947 ) = 0.3267
Reject null hypothesis if P value < level of significance
P - value = 0.3267 > 0.001 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

Test statistic is not in the critical region