SOLUTION: The pre-med adviser of a liberal arts college is trying to determine the proportion of students entering the pre-med program who gain admission to medical school within 6 years of
Question 335722: The pre-med adviser of a liberal arts college is trying to determine the proportion of students entering the pre-med program who gain admission to medical school within 6 years of entering the program.
a. If she does no preliminary study, how many former students from the pre-med program must she contact to be 90% sure that the point estimate is within 0.1 unit of p?
b. A random sample of 36 former students from the pre-med program showed that 24 entered medical school within 6 years from the time they entered the program. How many more must she contact to be 90% sure that the point estimate is within 0.1 unit of p? Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website! a. If she does no preliminary study, how many former students from the pre-med program must she contact to be 90% sure that the point estimate is within 0.1 unit of p?
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This implies you have no prior knowledge of the "ball park" level of the proportion of students gaining admission. In such cases, you use the conservative value of p=0.5 (because being Binomial in nature, its variance is highest at p=0.5)
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formula for required sample size is derived from the Margin of Error for a Normal approximation: and solving for n
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Given 90% confidence and assuming Normal approximation, Z=-\+1.645 since we need whole numbers round up to 68
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b. A random sample of 36 former students from the pre-med program showed that 24 entered medical school within 6 years from the time they entered the program. How many more must she contact to be 90% sure that the point estimate is within 0.1 unit of p?
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Having done a preliminary study, you have prior "ball park" knowledge of p.
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Same as part a) but substitute p=24/36=0.67 instead of p=0.5