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A poll of 1400 randomly selected students in grades 6 through 8 was conducted and found that 30% enjoy playing sports. Would confidence in the results increase if the sample size were 3200 instead of 1400? Why or why not?

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Solution Summary

The solution calculates confidence intervals for different sample sizes.

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sample proportion= 30%
We have to estimate the population proportion from the sample proportion.
This will lie in a range called the confidence limits.
We have to calculate confidence interval for sample sizes
n= 1400
and
n= 3200
at the same level of significance alpha (a) , say = 5%

Confidence limits when n= 1400
p= 30.00%
q=1-p= 70.00%
n=sample size= 1400
sp=standard error of proportion=square root of (pq/n)= 1.23% =square root of ( ...

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