Question

Based on historical data in Oxnard college, we believe that 42%
of freshmen do not visit their counselors regularly. For this year,
you would like to obtain a new sample to estimate the proportiton
of freshmen who do not visit their counselors regularly. You would
like to be 99% confident that your estimate is within 1% of the
true population proportion. How large of a sample size is required?
**Do not round mid-calculation.**

Answer #1

Sample size is given by the formula -

Where, E is the margin of errror = 1% = 0.01

p is the prior estimate of the population proportion = 42% = 0.42

Here, confidence level = 99% = 0.99

So, level of significance = = 1 - 0.99 = 0.01

is the critical value of z for two tailed test at 0.01 level of significance = 2.58 [can be obtained from the z table by finding the z for which area is approximately equal to 0.005 (as it is two tailed test)]

So, the sample size will be -

= 16214.99

~ 16215

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