Question

A student is interested in the mean life span of males in his town. He has heard claims that the mean age at death for males in his town is 70 years, but suspects that it is less. He randomly selects 88 male death records from the past year. The mean age at death for these 88 men was 68.9 years, with a standard deviation of 16.71 years. Test the student's claim at the 0.05 level of significance.

What are we looking for and what are we going to do with this?

Answer 1

To test the student's claim, we will conduct a hypothesis test using the 0.05 level of significance. The null hypothesis is that the mean age at death for males in the town is 70 years, while the alternative hypothesis is that it is less. Using the z-test and the given data, we calculate the test statistic and compare it to the critical value to make a decision.

Step-by-step explanation:

To test the student's claim, we will conduct a hypothesis test using the 0.05 level of significance.

Step 1: State the null and alternative hypotheses:

H0: The mean age at death for males in the town is 70 years
H1: The mean age at death for males in the town is less than 70 years

Step 2: Determine the test statistic and critical value:

Since the sample size is large (n > 30) and the population standard deviation is known, we can use a z-test. The test statistic is calculated as:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

In this case, the test statistic is z = (68.9 - 70) / (16.71 / sqrt(88)).

Using a significance level of 0.05, the critical value for a one-tailed test is -1.645.

Step 3: Calculate the test statistic and make a decision:

Calculating the test statistic, we find that z = -1.71.

Since the test statistic (-1.71) is less than the critical value (-1.645), we reject the null hypothesis. This means that there is evidence to support the student's claim that the mean age at death for males in the town is less than 70 years.