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ps://colostate.instructure.com/courses/74989/quizzes/114988/take To investigate possible gender discrimination in a firm, a sample of 100 men and 64 women with simillar job descriptions are selected at random. A summary of the resulting monthly salaries follows Average salary Standard deviation (syl Men $3100 $200 100 Women $2900 320 64 Do these data represent statistically significant evidence that average wages of men and women are different at this firm Answer the question by colculating and interpreting the relevant t-statistic. Show your work to get full points. HTML Editor? . Paragraph - 0 words Quiz saved at 11:45am Submit Quiz rch

Solution

ANSWER:

HO : MIU M - MIU F = 0

H1 : MIU M - MIU F NOT EQUAL TO 0.

T statistic = average salary of men - average salary of women - 0 / ( ( std of men) ^ 2 / no of of obsevations of m + ((std of women) ^ 2 / no of observations of women) ) ^ 1 / 2

t statistic = 3100 - 2900 - 0 / ( ( 200) ^ 2 / 100 +( (320) ^ 2 / 64) ) ^ 1 / 2

t statistic = 200 / ( 400 + 1600) ^ 1/2

t statistic = 200 / 44.72 = 4.47

degree of freedom = no of obsevation of men + no of observation of women - 2 = 100 + 64 - 2 = 162

we will use normal distribution and the critical value a 1% significance level in a two tailed test is 2.58 and therefore we reject ho at 1% and therefore there is a statistically significant difference between the salaries of men and women.