Q.12 - The Practice of Statistics for AP

Question

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 $6.208\pm 1.96\frac{0.372}{\sqrt{47}}$. Explain why this interval is wrong. Then give the correct interval.

Step-by-Step Solution

Answer

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

b. The confidence interval is$(5.4565,6.9594)$

step 1: introduction

Collected data from an SRS of $48$ out of the over $700000$ South 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 $2.567$

step 2: explanation part (a)

we have,

sample standard deviation s =$2.567$

sample size n =$48$ and sample mean$\stackrel{-}{x}=6.208$

The normal condition is met in this case because to build the confidence interval either the sample size ought to be at least$30$or the population should be distributed typically as the sample size is over $30$.$30$

step 3: explanation part (b)

Calculating confidence interval by using

sample standard deviation s =$2.567$

sample size n = $48$ and sample mean $\stackrel{-}{x}=6.208$

CI = $6.208\pm 2.021\frac{2.567}{\sqrt{48}}$

 Hence the confidence interval is $(5.4565,6.9594)$