Question

According to the editor of Beautiful Bride magazine, Betty Bridegroom, the average age of a groom is now 26.2 years (µ = 26.2).  A sample of 16 prospective grooms (n = 16) in Chicago revealed that their average age was 28.2 years (X = 28.2) with a standard deviation of 5.3 years (s = 5.3).  Is there enough evidence to claim that the Chicago groom’s age is greater than the age reported by Betty?

Conduct a hypothesis test, use the traditional method to solve this problem using α = 0.01.

Make sure you provide all 5 steps of your hypothesis test.

Answer 1

The null and alternative hypothesis for the test is:

; i.e., the true mean age of Chicago groom is 26.2 years.

; i.e., the true mean age of Chicago groom is greater than 26.2 years.

At significance level of we need to test this hypothesis.

Given:

Sample mean,

Sample standard deviation,

Sample size,

Population mean.

Test-statistic:    The formula for test-statistic is

Degrees of freedom:

Calculation for test-statistic-

So, the test-statistic is calculated as

Now, we have to find the p-value for the test-statistic we have calculated in order to make the decision. whether we reject or don not reject null hypothesis.

P-value:

So, the p-value for the test-statistic is calculated as

___________________________________

Decision: Now by comparing the p-value and the significance level we make a decision, since we are conducting a Right-tailed hypothesis.

Since,

Conclusion: At the sample data provides insufficient evidence to reject null hypothesis H₀ . So, we did not have enough evidence to believe that the true mean age of Chicago groom is greater than 26.2 years.

In other words, at significance level of the sample data does not provide enough evidence to support alternative hypothesis H₁ , hence we fail to reject null hypothesis H₀ and conclude that, we did not have evidence to believe that the true mean age of Chicago groom is greater than 26.2 years.