Question

Only part e) please

4. The following table contains the wages and gender for 6 emplovees at company X. female name Claire Matt Bruce Susan Tom Jennifer wage 14 18 0 16 0 a) Compute the sample mean, variance and standard deviation of wages. b) Compute the mean of the variable female. [Side note: notice that the mean of a dummy variable is equal to the share of observations for whom the variable equals 1.] c) Express the following statements as a null vs. an alternative hypothesis: i. The mean wage at company X equals $10 ii. The mean wage at company X is greater than $12 iii. Mean wages for men and women are the same at company X d) i. ii. iii. Test each of the hypothesis in question 4.c above, and state whether you reject the nulls with 95% confidence. Use the t-test formula covered in lecture. e) Let Ho be the value of a null hypothesis regarding the mean wage at company X (for all employees). What is the minimum value of 140 (rounded to 2 decimals) such that you would not reject the hypothesis that mean wage at company X equals 140 against the alternative that the mean wage is different from with 5% significance? 1. ii. What is the maximum value of uo (rounded to 2 decimals) such that you would not reject the hypothesis that mean wage at company X equals μ0 against the alternative that the mean wage is different from μ0 with 5% significance? Based on your results from the last two questions (4.e.i and 4.e.ii), construct the 95% confidence interval for the mean wage at company X. iii.

Answer 1

For part e

The answers for (i,ii & iii) are calculated through one formula as below

.ThL ].mnd er denadexce ivkruals $. A populakien mean Jerend Deroud a M puieu mean z table is used s 4.73 0sing t-talle , ualle 4 t af qSY. Cl .andd)-(6-1)-3 (95%) 12 + 2,541|VHT CI (703 / 16.qq

e i = 7.03

e ii = 16.97

CI = (7.03, 16.97)

All calculations are done with 95% confidence interval and 5% level of significance (alpha)