Chapter 10.2, Problem 46E

a.

To determine

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

Answer to Problem 46E

Yes.

Explanation of Solution

Given:

  $\begin{array}{cccc}\text{Group}& n& \overline{x}& s_x\\ \text{Anglo}& 92& 6.37& 0.60\\ \text{Hispanic}& 86& 5.91& 0.93\end{array}$

Formula used:

The formula to compute the confidence interval is:

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

Here, it is given that the sample sizes are 92 and 86 respectively which are above the required sample size of 30 which implies that the distribution is normally distributed. Thus, the two-sample procedure could be used here

b.

To determine

To find: The 90% confidence interval for the difference between the mean ratings and interpret it.

Answer to Problem 46E

The confidence interval is (413.62, 634.64).

Explanation of Solution

Calculation:

The 95% confidence interval for the difference between the mean ratings using Ti-83 calculator can be calculated as:

  

Thus, the confidence interval is (0.2264, 0.6936).

Interpretation:

There is 95% probability that the mean difference between the ratings 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 95% of the samples have confidence interval that are containing the mean difference of the ratings of the reliability for Hispanic and Anglo customers of bank.