Question

Question 4 3 pts In a previous study of body temperatures of 106 adults at midnight, with a range from 96.5°F to 99.6°F. Find the minimum sample size required to estimate the mean body temperature of all adults. Assume that we want 96% confidence that the sample mean is within 0.08 F of the population mean. A. Find the sample size using the range rule of thumb to estimate o. B. n Assume that o=0.65 based on the actual calculation from the 106 adults. n C. Compare the results from parts (A) and (B). Which result is likely to be better? i. Part (A) results will likely be better. ii. Part (B) results will likely be better. iii. Both results should be similar. iv. There is no way to predict before the studies are done. v. None of the above. В І U HTML Editor A

Answer 1

Given : Margin of error=E=0.08

Significance level=$\alpha$=0.04

Now , the critical value is , $Z_{\alpha/2}=Z_{0.04/2}=2.05$ ; From Z-table

A. Now , the range is given by ,

Range = Largest observation - Smallest observation = 99.6-96.5=3.1

By using range rule of thumb , the standard deviation is ,

3.1 o Range 4. - 0.7750

Therefore , the required sample size is ,

$n=(\frac{Z_{\alpha/2}*\sigma}{E})^2=(\frac{2.05*0.7750}{0.08})^2\approx 394$

B. Since , $\sigma=0.65$

Therefore , the required sample size is ,

$n=(\frac{Z_{\alpha/2}*\sigma}{E})^2=(\frac{2.05*0.65}{0.08})^2\approx 277$

C.

i. Part (A) results will likely be better.