# Notes: indicates that the estimates are statistically significant at the 5 percent level1. Manually construct a 95% confidence interval for the change in women's average hourly earningsbetween 1992 and 20082. Manually construct a 95% confidence interval for the change in the gender gap in average hourlyearnings between 1992 and 2008. (hint portion in the second image attached)3. Based on the analysis answer the following questions:1. Is the gender gap large? Why?2. Did the estimated gender gap increased from 1992 to 2008? If so, how much? Is this increasestatistically significant at the 5% level?3. How large is the gender gap in 1992 and 2008 if it is measure in percentage terms? Do you thinkit is large? [Hint: What percent is the difference with respect to average men's earning? Manuallycalculate this percent and discuss.]MenWomenDifference between Men and Women95% CI forSE (-m(8)0.33differenceYearSm(2)10.17SW(5)7.87П(6)13681230(7)3.223.554.144.104.11*.indicates that the estimates are statistically significant at the 5 percent level.(1)23.27(3)1594(4)20.05(9)(2.58, 3.88[2.80, 4.19]3.32, 4.97(3.40, 4.803.41, 4.80]1992199622.4810.10137918.987,950.359.369.3620.74200024.8811.60130311810.420.360.35200425.121201189421.0217351871200824.9811.78183820.879.66Notes:

Question
105 views help_outlineImage TranscriptioncloseNotes: indicates that the estimates are statistically significant at the 5 percent level 1. Manually construct a 95% confidence interval for the change in women's average hourly earnings between 1992 and 2008 2. Manually construct a 95% confidence interval for the change in the gender gap in average hourly earnings between 1992 and 2008. (hint portion in the second image attached) 3. Based on the analysis answer the following questions: 1. Is the gender gap large? Why? 2. Did the estimated gender gap increased from 1992 to 2008? If so, how much? Is this increase statistically significant at the 5% level? 3. How large is the gender gap in 1992 and 2008 if it is measure in percentage terms? Do you think it is large? [Hint: What percent is the difference with respect to average men's earning? Manually calculate this percent and discuss.] Men Women Difference between Men and Women 95% CI for SE (-m (8) 0.33 difference Year Sm (2) 10.17 SW (5) 7.87 П (6) 1368 1230 (7) 3.22 3.55 4.14 4.10 4.11*. indicates that the estimates are statistically significant at the 5 percent level. (1) 23.27 (3) 1594 (4) 20.05 (9) (2.58, 3.88 [2.80, 4.19] 3.32, 4.97 (3.40, 4.80 3.41, 4.80] 1992 1996 22.48 10.10 1379 18.98 7,95 0.35 9.36 9.36 20.74 2000 24.88 11.60 1303 1181 0.42 0.36 0.35 2004 25.12 1201 1894 21.02 1735 1871 2008 24.98 11.78 1838 20.87 9.66 Notes: fullscreen
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Step 1

3.1 According to the provided data, the gender gap is provided as mean of man – mean of women. It indicates that all the estimates are statistically significant at 5% level of significance. It can be concluded that estimates are statistically significant and gender gap is large.

Step 2

3.2 The null and alternative hypotheses are:

Null hypothesis: The estimated gender gap is equal to zero.

Alternative hypothesis: The estimated gender gap is larger than zero.

The test statistic can be obtained as: help_outlineImage Transcriptionclose(F-Y -99244 (Y-Y 2008 (T-F208-2 w1992 t= SE(T-F) +SE (Y-Y 2008 SE(YY 1992 (4.11-3.22)-0 0.33+0.35 =1.3088 fullscreen
Step 3

The degrees of freedom = 1594+1368+1838+1871-2 = 6669.

Using the t-distribution table, the t-critical value is obtained as 1.645 which is greater than the calculated test statistic. The null hypothe...

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