Question

Prices of New Mobile Homes. Recall that a simple random sample of 36 new mobile homes yielded the prices, in thousands of dollars, shown in Table $8.1$on page 315 . We found the mean of those prices to be $\backslash (63.28$thousand.

a. Use this information and Procedure $8.1$on page 322 to find a $95\%$confidence interval for the mean price of all new mobile homes. Recall that $\sigma =\backslash )7.2$thousand.

b. Compare your $95\%$confidence interval in part (a) to the one found in Example 8.2(c) on page 317 and explain any discrepancy that you observe.

Short answer

(a) $95\%$confidence interval for $\mu$is $(60.928,65.632)$

(b) Above example provides $95\%$confidence interval.

Step-by-step solution

Given Information

It is given that$\overline{x}=563.28,n=36,\sigma =7.2$

Determination of 95% Confidence Interval of μ

From table, value of $z_{\frac{\alpha }{2}}=1.96$with $95\%$confidence interval.

Hence, $\overline{x}\pm z_{\frac{a}{2}}\left(\frac{\sigma }{\sqrt{n}}\right)=63.28\pm 1.96\left(\frac{7.2}{\sqrt{36}}\right)$

$=63.28\pm 2.352$

$=(60.928,65.632)$

Hence,$95\%$confidence interval of$\mu$is$=(60.928,65.632)$

Comparison of confidence interval here with that of example 8.2(c)

The confidence level from example is $(60.88,65.68)$

In above part, confidence interval is $\left(60.88,65.88\right)$

Hence, it can be concluded that example provides approximately $95\%$confidence interval.