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Q.11

Expert-verifiedFound in: Page 622

Book edition
4th

Author(s)
David Moore,Daren Starnes,Dan Yates

Pages
809 pages

ISBN
9781319113339

**Who uses instant messaging?** Do younger people use online instant messaging (IM) more often than older people? A random sample of IM users found that $73$ of the $158$ people in the sample aged $18$ to $27$ said they used IM more often than email. In the $28$ to $39$ age group, $26$ of $143$ people used IM more often than email.$9$ Construct and interpret a $90$% conﬁdence interval for the difference between the proportions of IM users in these age groups who use IM more often than email.

From the given information, it could be interpreted that there is $90\%$ the probability that the difference in the proportion of IM users lies between $0.1959$ and $0.3641$

It is given in the question that, ${x}_{1}=73,{n}_{1}=158,{x}_{2}=26,{n}_{2}=143$

The formula to compute the confidence interval for the difference in population proportion is :

$CI=({\hat{p}}_{1}-{\hat{p}}_{2})\pm {z}_{\alpha /2}\times \sqrt{\frac{{\hat{p}}_{1}(1-{\hat{p}}_{1})}{{n}_{1}}+\frac{{\hat{p}}_{2}(1-{\hat{p}}_{2})}{{n}_{2}}}$

The $95\%$ confidence interval using Ti-$83$ plus calculator is computed as:

Therefore, the confidence interval is ($0.1959,0.3641$)

Therefore, it could be interpreted that there is $90\%$ probability that the difference in the proportion of IM users lies between $0.1959$ and $0.3641$

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