Question

Chapter 8 Confidence: X Connect Maryland Sec. X M Inbox - brentspoonere X M Inbox - trinigizmo@gm X Meet-ja-zgcc-zo X c.instructure.com/courses/20438/assignments/257908 Plus Due Sunday by 11:59pm Points 2 Submitting an external tool Available Jul 7 at 12am Aug 2 at 11:59pm 27 uncements as Chapter 8 Confidence Intervals (Mean) Done bus Score: 274 3/4 answered ules Question 4 < > B0/1 pt o gnments cussions The body temperatures in degrees Fahrenheit of a sample of adults in one small town are: 99.6 99.5 97.6 96.6 96.3 97.7 96.7 99.3 98.9 97.2 98.8 99.4 s dent Support Assume body temperatures of adults are normally distributed. Based on this data, find the 90% confidence interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population. coring Services 90% C.I. - ansfer Services Basic Funcs Trig Interval ✓ 1 T DNE Enter an intervalsing interval rotation more.] B 7 B

Answer 1

Answer:

$\text{90\% CI}=(97.486,98.780)$

Explanation:

The confidence interval for the mean is obtained using the following formula,

$\text{90\% CI}=\overline{x}\pm t_c\times \frac{s}{\sqrt{n}}$

The sample mean and the sample standard deviation values are obtained in excel using the function =AVERAGE() and =STDEV() respectively.

The t critical value is obtained from t distribution table for significance level = 0.10 and degree of freedom = n -1 = 12 - 1 = 11.

$t_c=t_{\alpha/2,n-1}=t_{0.10/2,11}=t_{0.05,11}=1.796$

now,

$\text{90\% CI}=98.133\pm 1.796\times \frac{1.248}{\sqrt{12}}$

$\text{90\% CI}=(97.486,98.780)$

The calculations are done in excel. The screenshot is shown below,

D2 1 x ✓ fc =AVERAGE(A2:A13) A B 1 Temperature 2 99.6 3 99.5 с E Temperature Excel function Sample mean 98.133 AVERAGE(A2:A13) Sample std dev 1.248 STDEV(A2:A13) Sample size 12 COUNT(A2:A13) df 11 D4-1 alpha 0.1 t critical 1.796 T.INV.2TD6, D5) 4 97.6 5 96.6 96.3 6 97.7 7 8 9 96.7 99.3 98.9 97.2 lower limit upper limit 97.486 D2-D7*D3/SQRT(D4) 98.780 D2+D7D3/SQRT(D4) 10 11 12 98.8 13 99.4