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Chapter 8: Q.12 (page 525)

How many people live in South African households? To find out, we collected data from an SRS of 48 out of the over 700,000 South African students who took part in

the CensusAtSchool survey project. The mean number of people living in a household was 6.208; the standard deviation was 2.576.

(a) Is the Normal condition met in this case? Justify your answer.

(b) Maurice claims that a 95% confidence interval for the population mean is 6.208卤1.960.37247. Explain why this interval is wrong. Then give the correct interval.

Short Answer

Expert verified

a. Yes, the Normal condition is met in this case

b. The confidence interval is(5.4565,6.9594)

Step by step solution

01

introduction

Collected data from an SRS of 48out of the over 700000South African students who took part in the Census At School survey project.

The mean number of people living in a household was 6.208; the standard deviation was 2.567

02

explanation part (a)

we have,

sample standard deviation s =2.567

sample size n =48and sample meanx-=6.208

The normal condition is met in this case because to build the confidence interval either the sample size ought to be at least30or the population should be distributed typically as the sample size is over 30.30

03

explanation part (b)

Calculating confidence interval by using

sample standard deviation s =2.567

sample size n = 48and sample meanx-=6.208

CI = 6.208卤2.0212.56748

Hence the confidence interval is(5.4565,6.9594)

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