Question

Part 1

A, You are testing H0: μ=100   vs   H1: μ>100 , using a sample of n=20 . The test statistic is ttest=2.15 . The P value should be:

1. 0.02232
2. 0.97768
3. 0.02198

B. You are testing H0: μ=15   vs   H1: μ≠15 , using a sample of n=8 . The 95% t Confidence Interval for μ is 17, 23 . The P value of the test could be:

1. 0.9750
2. 0.0500
3. 0.0002

C. You are testing H0: μ=50   vs   H1: μ<50 , using a sample of n=15 . The 95% t Confidence Interval for μ is 35, 85 . The P value of the test could be:

1. 0.9750
2. 0.0500
3. 0.0002

D. You are testing H0: μ=50   vs   H1: μ<50 , using a sample of n=12 . The P value of the test is 0.0003 . A possible 95% t confidence interval is:

1. 42, 56
2. 29, 46
3. 55, 69

E. You are testing H0: μ=10   vs   H1: μ>10 , using a sample of n=25 . The P value of the test is 0.049 . A possible 95% t confidence interval is:

1. 5.5, 13.9
2. 25.7, 33.4
3. 10.1, 18.7

Answer 1

Q1) For n - 1 =19 degrees of freedom, the p-value here is obtained from t distribution tables as: (For right tailed test as seen from alternative hypothesis)

p = P( t₁₉ > 2.15) = 0.02232
Therefore 0.02232 is the required p-value here.

Q2) As the 95% confidence interval here is 17, 23 and 15 does not in the interval, therefore the null hypothesis could be rejected at the 5% level of significance which means that the p-value < 0.05.

Therefore c) 0.0002 is the required p-value here.

Q3) Here, the 95% confidence interval is 35, 85. As 50 lies in the given confidence interval, therefore we cannot reject the null hypothesis here at the 5% level of significance. Therefore p-value > 0.05 here.

Therefore a) 0.975 is the required p-value here.

Q4) As the p-value here is 0.0003 < 0.05. Therefore the test is significant here and so the 95% confidence interval wont contain the hypothesized value of 50 here and also as the test is significant therefore the whole confidence interval should lie below 50 ( as this is a left tailed test )

Therefore (29, 46) is the required confidence interval here.

Q5) As the p-value here is 0.049 < 0.05, therefore the test is significant here and 10 should not lie in the confidence interval, also as we are testing whether mean is more than 10, therefore the whole confidence interval here should lie above 10.

Therefore 10.1, 18.7 is the required confidence interval here.