# Sample size

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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 Preview

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 ( ...

#### Solution Summary

The solution calculates confidence intervals for different sample sizes.

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