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Chapter 9: Q.81 (page 590)

Refer to Exercise 79. Construct and interpret a 95%confidence interval for the population mean M. What additional information does the confidence interval provide .

Short Answer

Expert verified

The confidence interval is (11.561,11.472).

Step by step solution

01

Given information

From question 79, The hardness data for a random sample of 20tablets are

02

Explanation


11.267


11.613
11.493
11.602
11.36
11.374
11.592
11.458
11.552
11.463
11.383
11.715
11.485
11.509
11.429

11.477

11.57
11.623
11.472
11.531
03

Calculate the confidence interval

The confidence interval for population mean is:

x炉-t伪/2脳sn<渭<x炉+t伪/2脳sn

The sample mean and standard deviation are 11.5164and 0.0950.

Degree of freedom:

localid="1650359464291" role="math" df=n-1=20-1=19

From critical value table, the t-value is 2.093.

The confidence interval is computed as:

x炉-t伪/2脳sn<渭<x炉+t伪/2脳sn

11.5164-2.096脳0.095020<渭<11.5164+2.096脳0.095020

(11.561,11.472)

The confidence interval is (11.561,11.472).

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