Question

According to a new report from the Wall Street Journal, female real estate agents sell more homes per year than male real estate agents do. You, the head of a large real estate company, want to know if this is true within your organization, so you sample 55 women and 37 men. From the sample, you find that the female agents sell an average of 25.2 homes per year with a standard deviation of 7.7 homes. The male agents sell an average of 22.9 homes per year with a standard deviation of 6.3 homes. Let females be population 1 and males be population 2 and assume the population variances are equal. Use a significance level of 0.05.

Calculate the appropriate test statistic needed to test your claim. Round your final answer to 4 decimals. Hint: Make sure you are using the correct formula based on the information given in the problem.

Find and enter the correct critical value needed to test your claim at the 5% significance level. Round your final answer to 4 decimals. Hint: Things you will need to know: alpha, df, is this one or two-tailed test, and which table to use!

Answer 1

From the information, observe that a new report from the Wall street journal, female real estate agents sells more homes per year than male real estate agents do Consider a random sample of 55 women with an average of 25.2 homes per year and standard deviation of 7.7 homes Consider a random sample of 37 men with an average of 22.9 homes per year and standard deviation of 6.3 homes Consider X, is the variable that represents the women and X, is the variable that represents the men Assume that the population variances are equal The sample information is as follows: Women Men 25.2 22.9 6.3 Average 37 The null and Alternative hypothesis is as follows Null hypothesis, Ho: The average sell homes by the female real estate agents is not more than the average sell homes by the male real estate agents Alternative hypothesis, H The average sell homes by the female real estate agents is more than the average sell homes by the male real estate agents Calculate the pooled standard deviation. 55-1)(7.7)+(37-1) (6.3 55 +37 -2 - V51.45 7.173

Calculate the test statistic 25.2 -22.9 7.173 55 37 2.3 1.52515 1.5080 The level of significance is. a0.05 The degrees of freedom are, 55 +37-2 - 92-2 -90 This test is one tail test because the alternative hypothesis is more than type Use standard t tables because the population standard deviations are not given From the standard t table values, observe that the critical value of t for the one tail (right tail) test at 5% level of significance and 90 degrees of freedom is 1.6620 Compare the calculated value with the critical value Here, the calculated value less than the critical value so fails to reject the Null hypothesis Hence, conclude that there is insufficient evidence that the average sell homes by the female real estate agents is more than the average sell homes by the male real estate agents