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Question 4 [1.0+0.3 pts: a, b (0.5 points each), c (optional, 0.3 pts)] To investigate the possibility of gender discrimination in a firm, a sample of 100 men and 64 women with similar job descriptions are selected at random. A summary of the resulting monthly salaries follows: Table 2: Monthly Salary of Men and Women Workers Average Salary (Y) Standard Deviation (sy) Sample Size Men Women $3100 $3000 $200 $200 100 64 (a) You wanted to test if there is difference in average salaries of male and female workers, i.e. $H_0: \mu_{men} = \mu_{women}$ (or $\mu_{men} - \mu_{women} = 0$) versus $H_a: \mu_{men} \neq$ $\mu_{women}$ (or $\mu_{men} - \mu_{women} \neq 0$). Using the normal approximation ($t_{crit} \approx 1.96)$, (i) construct a 95% confidence interval for the difference in average salaries and (ii) decide whether or not you can reject $H_0$. (b) At the significance level, $\alpha = 0.05$, (i) compute t-stat, (ii) obtain the P-value of your t-stat, and (iii) provide your conclusion based on the hypotheses specified in (a). (c) Is it enough to conclude that there is gender discrimination in this labor market? Explain. If there is something lacking, what is it? If there is not, why is this evidence sufficient? (Hint: Think about the concept of \"all other things are equal\" and this test-setting).

          Question 4
[1.0+0.3 pts: a, b (0.5 points each), c (optional, 0.3 pts)] To investigate the possibility of
gender discrimination in a firm, a sample of 100 men and 64 women with similar job descriptions
are selected at random. A summary of the resulting monthly salaries follows:
Table 2: Monthly Salary of Men and Women Workers
Average Salary (Y) Standard Deviation (sy) Sample Size
Men
Women
$3100
$3000
$200
$200
100
64
(a) You wanted to test if there is difference in average salaries of male and female
workers, i.e. $H_0: \mu_{men} = \mu_{women}$ (or $\mu_{men} - \mu_{women} = 0$) versus $H_a: \mu_{men} \neq$
$\mu_{women}$ (or $\mu_{men} - \mu_{women} \neq 0$). Using the normal approximation ($t_{crit} \approx 1.96)$, 
(i) construct a 95% confidence interval for the difference in average salaries
and (ii) decide whether or not you can reject $H_0$.
(b) At the significance level, $\alpha = 0.05$, (i) compute t-stat, (ii) obtain the P-value of
your t-stat, and (iii) provide your conclusion based on the hypotheses specified
in (a).
(c) Is it enough to conclude that there is gender discrimination in this labor market?
Explain. If there is something lacking, what is it? If there is not, why is this
evidence sufficient? (Hint: Think about the concept of \"all other things are
equal\" and this test-setting).

Question 4
[1.0+0.3 pts: a, b (0.5 points each), c (optional, 0.3 pts)] To investigate the possibility of
gender discrimination in a firm, a sample of 100 men and 64 women with similar job descriptions
are selected at random. A summary of the resulting monthly salaries follows:
Table 2: Monthly Salary of Men and Women Workers
Average Salary (Y) Standard Deviation (sy) Sample Size
Men
Women
31003000
200200
100
64
(a) You wanted to test if there is difference in average salaries of male and female
workers, i.e. H0: μmen = μwomen (or μmen - μwomen = 0) versus Ha: μmen≠
μwomen (or μmen - μwomen≠ 0). Using the normal approximation (tcrit≈ 1.96),
(i) construct a 95% confidence interval for the difference in average salaries
and (ii) decide whether or not you can reject H0.
(b) At the significance level, α = 0.05, (i) compute t-stat, (ii) obtain the P-value of
your t-stat, and (iii) provide your conclusion based on the hypotheses specified
in (a).
(c) Is it enough to conclude that there is gender discrimination in this labor market?
Explain. If there is something lacking, what is it? If there is not, why is this
evidence sufficient? (Hint: Think about the concept of äll other things are
equaländ this test-setting).

Added by Crystal D.

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