Answer in Statistics and Probability for John #251274
The following null and alternative hypotheses need to be tested:
“H_0:mu=1500”
“H_1:munot=1500”
This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is “alpha = 0.05, df=n-1”
“=200-1=199” degrees of freedom, and the critical value for a two-tailed test is“t_c = 1.971957.”
The rejection region for this two-tailed test is “R = {t: |t| > 1.971957}.”
The t-statistic is computed as follows:
“t=dfrac{bar{x}-mu}{s/sqrt{n}}=dfrac{1560-1500}{50/sqrt{200}}=16.970563”
Since it is observed that “|t|= 16.970563>1.971957=t_c” it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value for two-tailed, “alpha=0.05, df=199,” “t=16.97” is “papprox0,” and since “p=0<0.05=alpha,” it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean “mu” is different than 1500, at the “alpha = 0.05” significance level.
