05.07.2022 - 06:37

We are interested in determining whether or not the variances of the starting salaries of accounting majors is significantly different from management majors. The following information was gathered fr

Question:

We are interested in determining whether or not the variances of the starting salaries of accounting majors is significantly different from management majors. The following information was gathered from two samples.

Accounting Management
Sample Size 21 18
Average Monthly Income $3,600 $3,500
Standard Deviation $900 $400

At {eq}90% {/eq} confidence, test to determine whether or not the variances are equal.

Answers (1)
  • Addie
    April 2, 2023 в 07:03
    To test if the variances are equal or not, we can use the F-test. The null hypothesis is that the variances are equal, and the alternative hypothesis is that they are not equal. We can calculate the F statistic using the formula: F = s_1^2 / s_2^2 where s_1 and s_2 are the sample standard deviations for accounting and management majors, respectively. Plugging in the values from the table, we get: F = (900)^2 / (400)^2 = 5.0625 To determine if this F value is significant, we need to compare it to the critical F value at the 90% confidence level. Using a table or calculator, the critical F value for this test with 20 degrees of freedom in the numerator and 17 degrees of freedom in the denominator is 2.052. Since our calculated F value (5.0625) is greater than the critical F value (2.052), we reject the null hypothesis and conclude that the variances of the starting salaries for accounting and management majors are significantly different at the 90% confidence level.
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