(Solved): Suppose you conduct a t-test for the null hypothesis \( H_{0}: \mu=100 \) versus the alternative hy ...

Suppose you conduct a t-test for the null hypothesis \( H_{0}: \mu=100 \) versus the alternative hypothesis \( H_{a}: \mu<100 \) based on a sample of 16 observations. The test results are \( t=-1.84 \) and \( p \)-value \( =0.043 \). a. What assumptions are necessary for the validity of this procedure? b. Interpret the results of the test. c. Suppose the alternative hypothesis had been the two-tailed \( \mathrm{H}_{\mathrm{a}}: \mu \neq 100 \). If the \( \mathrm{t} \)-statistic were unchanged, then what would the p-value be for this test? Interpret the p-value for the two-tailed test. a. Select all that apply. A. A random sample is selected from the target population. B. The population from which the sample is selected has a distribution that is approximately normal. C. The population standard deviation is approximately equal to the sample standard deviation. D. No assumptions need to be made to perform the test.