Question

Student is interested in the mean lifespan of males in his town he has heard claims that the mean age of death for males in his town is 70 years at six facts that it is less he randomly selects 88 mills deaths from the past year the mean age at death for these 88 men with 68.9 years with a standard deviation of 16.71 years test the students claim at the 0.05 level of significance

Answer 1

The provided sample mean is and the sample standard deviation is s=16.71, and the sample size is n=88.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation, will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a left-tailed test is

tc​=−1.663.

The rejection region for this left-tailed test is R=t:t<−1.663

(3) Test Statistics

The t-statistic is computed as follows:

(4) The decision about the null hypothesis

Since it is observed that t=−0.618≥tc​=−1.663, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.2692, and since p=0.2692≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is less than 70, at the 0.05 significance level.

Graphically

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!