Salary information regarding two independent random samples of male and female employees of a large company is shown below.

Male

Female

Sample size

64

99

Sample mean salary (in $1000s)

440

410

Population variance

888

999

If you are interested in testing whether the average salary of males is significantly greater than that of females, the value of the test statistic is _____.

Question

Salary information regarding two independent random samples of male and female employees of a large company is shown below.

Male

Female

Sample size

64

99

Sample mean salary (in $1000s)

440

410

Population variance

888

999

If you are interested in testing whether the average salary of males is significantly greater than that of females, the value of the test statistic is _____.

BlackTom AI · Accepted Answer

The problem asks for the value of the test statistic when testing whether the average salary of males is significantly greater than that of females.

First, let’s restate the available data: sample sizes are n_m = 64 for males and n_f = 99 for females; sample means are xbar_m = 440 (in $1000s) and xbar_f = 410; population variances are sigma_m^2 = 888 and sigma_f^2 = 999.

Since the question provides population variances, we treat this as a z-test for the difference between two means with known variances. The statistic for testing H0: mu_m - mu_f = 0 against the alternative mu_m > mu_f is:

z = (xbar_m - xbar_f) / sqrt( sigma_m^2 / n_m + sigma_f^2 / n_f )

Compute the components:
- Difference in means: xbar_m - xbar_f = 440 - 410 = 30 (in $1000s).
- Variance of the difference: sigma_m^2 / n_m + sigma_f^2 / n_f = 888/64 + 999/99.
  888/64 = 13.875.
  999/99 ≈ 10.0909.
  Sum ≈ 23.9659.
- Standard error (sqrt of the above): sqrt(23.9659) ≈ 4.895.

Now place into the formula:
z ≈ 30 / 4.895 ≈ 6.13.

Therefore, the test statistic value is approximately 6.13 (to three significant figures).

Note on the missing answer choices: The provided data section shows an empty list for answer_options. If this were a multiple-choice item, you would select the option that matches z ≈ 6.13. Since no explicit options are given here, we present the computed value and the method used to obtain it, so you can compare against any corresponding choice in your materials.

22803 Quantitative Skills in Accounting and Finance - Autumn 2025 Quiz 4

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