Question

The mean result of some observations was 50. Let $LaTeX: \mu$ μ denote the true mean result. We wish to test the hypothesis $LaTeX: H_0 \colon \mu =40$ H 0 : μ = 40 vs $LaTeX: H_a \colon \mu < 40$ H a : μ < 40 . Without doing any calculations, the p-value and test conclusion are most likely

Group of answer choices

Close to 0 so reject the null hypothesis

Close to 1 so fail to reject the null hypothesis

Close to 0 so fail to reject the null hypothesis

Close to 1 so reject the null hypothesis

Answer 1

Solution:

Given:

Sample mean =

T= 50

We have to test the hypothesis:

H₀ : μ = 40 vs    H_a : μ < 40

Since we have to test population mean μ < 40 and we have sample mean 50 which is > 40

Thus corresponding test statistic value would be positive and thus definitely p-value would be greater than 0.5. Since probability sample mean   less than population mean 40 is 50% and if sample mean is more than 40 , which is 50, then probability of sample mean is less than 50 would be greater than 0.5, thus it maybe close to 1 but not to 0.

Since P-value is larger and greater than 0.05 significance level, we fail to reject null hypothesis H0.

Thus correct option is:
Close to 1 so fail to reject the null hypothesis