Poverty and Dietary Calcium. Refer to Exercise 8.70.

a. Find a $90\%$confidence interval for $\mu$.

b. Why is the confidence interval you found in part (a) shorter than the one in Exercise 8.70?

c. Draw a graph similar to that shown in Fig$8.6$ on page 326 to display both confidence intervals.

d. Which confidence interval yields a more accurate estimate of $\mu$? Explain your answer.

Confidence level given is$90\%,95\%$

Follow following steps in MINTAB:

• Click Stat > Basic Statistics > 1-Sample C
• In Samples of column, click CALCIUM column.
• Enter $180$in standard deviation.
• Go through Options, enter Confidence level as $80$.
• In alternative, choose not equal.
• Press OK in all dialogue boxes.

From output of MINTAB, $90\%$confidence interval for $\mu$is$(874.502,1,020.276)$

It is due to the fact that $95\%$confidence level is used in Exercise 8.70.

In above part, $90\%$confidence level is used.

Also, width of interval is smaller if confidence level decrease.

For $90\%$confidence level of$\mu$

For $95\%$confidence level of$\mu$

Smaller confidence interval provide more accurate estimation. Hence, $90\%$confidence level provides more accurate estimation of$\mu$.