Answer
The null hypothesis gets rejected and concludes that population mean is not equal to 100.
Work Step by Step
The 100 random samples each of size 15 are generated in StatCrunch. The steps are as follows:
Step 1: Go to Data→Simulate→Normal.
Step 2: Write 15 under rows and 100 under columns.
Step 3: Write 100 under mean and 15 under standard deviation. In store samples, select split across columns.
Step 4: Finally, click compute and random numbers are generated.
To test the hypothesis for each of the 100 samples, the t-test is used. The null and alternative hypotheses are defined as
\[\begin{align}
& {{H}_{0}}:\mu =100 \\
& {{H}_{1}}:\mu \ne 100 \\
\end{align}\]
The t-test is applied to each sample with the help of StatCrunch. The steps are as follows:
Step 1: Go to stats→T-stats→One sample→with data.
Step 2: Under columns, select from Normal 1 to 100. Under Perform, write 100 in null hypothesis and not equals to 100 in alternative hypothesis. Then, finally compute.
The p-values of samples 45, 47, 6, 68, 93, 72, and 16 are 0.0094, 0.0133, 0.0354, 0.0389, 0.0457, 0.0481, and 0.0487, respectively. All are less than 0.05, so the null hypothesis gets rejected.
