Answer to Question #203568 in Statistics and Probability for Yumi Ramos

Question #203568

The operations manager of a sales company wants to see whether there is a significant difference in the ages of male and female customers. He selected a sample of 35 samples for each group. The ages are shown in the table below:


1
Expert's answer
2021-06-15T15:05:11-0400

Step 1:

The following null and alternative hypotheses need to be tested:

"H_0:\\mu_1=\\mu_2"

"H_1:\\mu_1\\not=\\mu_2"


Step 2:

This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations will be used.

Based on the information provided, the significance level is "\\alpha=0.05," and the critical value for a two-tailed test is "z_c=1.96."

The rejection region for this two-tailed test is "R=\\{z:|z|>1.96\\}"


Step 3:

The z-statistic is computed as follows:


"z=\\dfrac{\\bar{x}_1-\\bar{x}_2}{\\sqrt{\\sigma_1^2\/n_1+\\sigma_2^2\/n_2}}"

"=\\dfrac{27.3-28}{\\sqrt{2.4^2\/35+3.1^2\/35}}\\approx-1.05632"

Since it is observed that "|z|=1.05632<1.96=z_c," it is then concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean "\\mu_1" is different than "\\mu_2," at the "\\alpha=0.05" significance level.


Using the P-value approach: The p-value is "p=2P(Z>1.05632)=0.292057," and since "p=0.292057>0.05=\\alpha," it is concluded that the null hypothesis is not rejected. Therefore, there is not enough evidence to claim that the population mean "\\mu_1" is different than "\\mu_2," at the "\\alpha=0.05" significance level.



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