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21 votes
Suppose that 29\%29%29, percent of undergraduates at a large university are involved in a campus organization. The administration plans to take an SRS of 100100100 undergraduates from the population of over 20{,}00020,00020, comma, 000 undergraduate students at the school to see what proportion of students sampled are involved in a campus organization.

User Gcamargo
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2 Answers

7 votes
7 votes

Final answer:

The question pertains to college-level Mathematics, specifically inferential statistics, where the student needs to understand sampling techniques, calculate sample sizes for surveys, and interpret confidence intervals.

Step-by-step explanation:

The subject of this question is Mathematics, specifically, it deals with statistics and sampling techniques which are used in the field of inferential statistics. The question involves determining the sample size necessary to estimate a proportion with a certain level of confidence and margin of error, as well as discussing sampling methods and calculating confidence intervals for proportions.

For example, to estimate the proportion of college students who voted in a particular election with a specified confidence level and margin of error, one would need to use a sample size calculator or apply the formula for estimating a proportion based on the desired level of confidence and margin of error. This involves understanding concepts like z-scores, standard deviation, and the central limit theorem.

Moreover, sampling methods such as simple random sampling (SRS) or proportionate random sampling are highlighted, along with discussing the implications of confidence intervals in the context of population parameters. This question is typical for a college-level statistics course that goes beyond the basics and into more applied inferential statistics.

User Jknotek
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3.0k points
21 votes
21 votes

Answer:

μ p ^ =0.29

σ p ^ = Square root[ ( (0.29)(0.71) )/100 ]

Step-by-step explanation:

The mean of the sampling distribution of a sample proportion is equal to the population proportion.

μ p ^ =p

The population proportion reported is 29%, so p=0.29p.

\mu_{\hat p}=p=0.29μ

μ p ^ = 0.29

Since σ p hat = sqare root [ ( p(1-p) )/ n]

After subsitution we get σ p ^ = Square root[ ( (0.29)(0.71) )/100 ]

User Levan
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2.9k points
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