A researcher was interested in comparing the salaries of female and male employees of a particular company.Independent random samples of 8 female employees (sample 1)and 15 male employees (sample 2)yielded the following weekly salaries (in dollars). $$\begin{array} { r | r r }
\text { Female } & \text { Male } & \
\hline 495 & 722 & 518 \
760 & 562 & 904 \
556 & 880 & 1150 \
904 & 520 & 805 \
520 & 500 & 480 \
1005 & 1250 & 970 \
743 & 750 & 605 \
660 & 1640 &
\end{array}$$ Determine a 98% confidence interval for the difference, $\mu _ { 1 } - \mu _ { 2 } ,$ between the mean weekly salary of all female employees and the mean weekly salary of all male employees.
A)(-$335,$111)
B)(-$158,$382)
C)(-$383,$159)
D)(-$431,$208)
E)(-$385,$164)

Question

A researcher was interested in comparing the salaries of female and male employees of a particular company.Independent random samples of 8 female employees (sample 1)and 15 male employees (sample 2)yielded the following weekly salaries (in dollars). $$\begin{array} { r | r r } 
\text { Female } & \text { Male } & \
\hline 495 & 722 & 518 \
760 & 562 & 904 \
556 & 880 & 1150 \
904 & 520 & 805 \
520 & 500 & 480 \
1005 & 1250 & 970 \
743 & 750 & 605 \
660 & 1640 &
\end{array}$$ Determine a 98% confidence interval for the difference, $\mu _ { 1 } - \mu _ { 2 } ,$ between the mean weekly salary of all female employees and the mean weekly salary of all male employees.
A)(-$335,$111)
B)(-$158,$382)
C)(-$383,$159)
D)(-$431,$208)
E)(-$385,$164)

Quizplus · Accepted Answer

To find the confidence interval, we need to calculate the point estimate (the difference between the sample means) and the margin of error.

Point estimate: 
x̄1 - x̄2 = $626.25 - $775.87 = -$149.62

Margin of error:

s1 = $207.73 and s2 = $243.01

√[(s1^2/n1) + (s2^2/n2)] = √[(207.73^2/8) + (243.01^2/15)] = $115.51

t-value: From t-distribution table for 21 degree of freedom and 0.01 level of significance, we get the t-value as 2.518.

Margin of Error = t-value x Standard Error = 2.518 x 115.51 = $291.16

Thus, the 98% confidence interval for the difference between the mean weekly salary of all female employees and the mean weekly salary of all male employees is:

(-$383, $159)

Therefore, the best choice is C.

A Researcher Was Interested in Comparing the Salaries of Female