Question

Module 5: Problem 13 Previous Problem Problem List Next Problem 15 (1 point) A page was randomly selected from each of 7 brochures for cancer patients published by the American Cancer Society and the National Cancer Institute. The pages were judged for readability, using standard readability tests. The reading grade levels are given below. Grade levels: 7, 11, 12, 6, 11, 13, 16 Construct a 99% confidence interval for the population mean readability level. Note: You can earn partial credit on this problem 57 67 77 m8x Preview My Answers Submit Answers You have attempted this problem 0 times. You have 5 attempts remaining. em 107 Email instructor som 12 / er 13 slem 14. zlom 15 Page at 012 OT WWK10 2017 therm version 2.1 The We Work Project Show All x Lecture 10L -S....pdf 26 MacBook Pro 000 esc 80 800 & # 3 $ 4 % 5 1 2 6 7

Answer 1

For given sample mean value is $\overline{x}=\frac{\sum x}{n}=10.857$

Create the following table.

data	data-mean	(data - mean)2
7	-3.8571	14.87722041
11	0.1429	0.02042041
12	1.1429	1.30622041
6	-4.8571	23.59142041
11	0.1429	0.02042041
13	2.1429	4.59202041
16	5.1429	26.44942041

Find the sum of numbers in the last column to get. $\sum (xi-\overline{x})^2=70.8571$

So standard deviation is

S Σ(ri – 7)2 η -1 = 3.437

t value for 99% CI is TINV(0.01,6)=3.707

So Margin of Error is $E=t*\frac{s}{\sqrt{n}}=3.707*\frac{3.437}{\sqrt{7}}=4.816$

So CI is $\overline{x} \pm E=10.857\pm 4.816=(6.041,15.673 )$