Chapter 10.2, Problem 45E

a.

To determine

To explain: Whether the two-sample procedure could be used here or not.

Answer to Problem 45E

Yes.

Explanation of Solution

Given:

  $\begin{array}{cccc}\text{Group}& n& \overline{x}& s_x\\ \text{Males}& 675& 1884.52& 1368.37\\ \text{Females}& 621& 1360.39& 1037.46\end{array}$

Formula used:

The formula to compute the confidence interval is:

  $\left({\overline{x}}_1-{\overline{x}}_2\right)\pm t_{\alpha /2,df}\times \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$

It is not possible for the earing to take the negative values and the value of the standard deviation is equal to the mean which implies that the distribution is skewed and the values are within 2 standard deviations of the mean which implies that the two-sample procedure could be used here.

b.

To determine

To find: The 90% confidence interval for the difference between the mean earnings of female and male at the university and interpret it.

Answer to Problem 45E

The confidence interval is (413.62, 634.64).

Explanation of Solution

Calculation:

The 90% confidence interval for the difference between the mean earnings of female and male at the university using Ti-83 calculator can be calculated as:

  

Thus, the confidence interval is (413.62, 634.64).

Interpretation:

There is 90% probability that the mean difference between the earning is between $413.62 and $634.64.

c.

To determine

To interpret: The confidence interval computed in above part.

Explanation of Solution

The confidence interval shows that on an average 90% of the samples have confidence interval that are containing the mean difference of the earning of the men and women.