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Chapter 8: Q 47. (page 523)

Prom totals Use your interval from Exercise 39 to construct and interpret a 90%

confidence interval for the total number of seniors planning to go to the prom.

Short Answer

Expert verified

There is 90%confidence that between462and618seniors in Tanya's school go to prom.

Step by step solution

01

Given Information

It is given that c=90%=0.90

x=36,n=50

For1-α=0.90, using probabilityza/2=1.645

02

Construct and interpret confidence interval

Conditions are:

Random: As samples are selected randomly, it is satisfied.

Independent: Sample of 50seniors is less than 10%of all population of all seniors. This condition is met.

Normal: There are 36success and 50-36=14failures which are greater than 10.

All conditions are fulfilled.

Sample proportion is calculated as: p^=xn

=3650=0.72

Margin of Error: E=zα/2×p^(1-p^)n

=1.645×0.72(1-0.72)50=0.1045

Confidence Interval: p^-E=0.72-0.1045=0.6155

p^+E=0.72+0.1045=0.8245

The confidence interval is(0.6155,0.8245).

As population consists of 750seniors,

750(0.6155)=461.625≈462

750(0.8245)=618.375≈618

There is 90%confidence that between462-618seniors that plan to go to prom.

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