Let 1 – 2 denote the parameter of interest and suppose you have calculated a 90%

Question

Let 1 – 2 denote the parameter of interest and suppose you have calculated a 90% confidence interval for this parameter to be (0.16, 0.174). Further suppose you now need to test the hypotheses H0: 1 – 2 = 0.170 vs. Ha: 1 – 2 0.170. Based on the 90% confidence interval, which of the following is a legitimate conclusion about these hypotheses? Select one or more: a. The p-value is larger than 0.10. b. The p-value is larger than 0.05. c. The p-value will be smaller than 0.10. d.The p-value will be smaller than 0.05. e.one of the statements above would be true about the confidence interval.

Explanation / Answer

The estimated difference between group means was 0.170

The upper and lower limits of a 90% Confidence intervaI are 0.16 and 0.174 respectively:

standard error (SE)is calculated as

SE=[0.174-(-0.16)]/(2*1.65) where 1.65 is the z table value for 90% CI

SE=0.1012

z=0.170/0.1012

z=1.68

p-value is computed as.

p=exp[(-0.717*z)-(0.416*z^2)]

p=exp[(-0.717*1.68)-(0.416*1.68^2)]

p-value=0.093<0.1

Hence ,the answer is option C.The p-value will be smaller than 0.10

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