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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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    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
    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.