 # S O C The fraternities and sororities at St. Algebra College have been plagued by declining membership over the past several years and want to know whether the incoming freshman class will be a fertile recruiting ground. Not having enough money to survey all 1600 freshmen, they commission you to survey the interests of a random sample. You find that 35 of your 150 respondents are “extremely” interested in social clubs. At the 95% level, what is your estimate of the number of freshmen who would be extremely interested? ( HINT: The high and low values of your final confidence interval are proportions. How can proportions be expressed as numbers? ) ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 6, Problem 6.17P
Textbook Problem
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## S O C The fraternities and sororities at St. Algebra College have been plagued by declining membership over the past several years and want to know whether the incoming freshman class will be a fertile recruiting ground. Not having enough money to survey all 1600 freshmen, they commission you to survey the interests of a random sample. You find that 35 of your 150 respondents are “extremely” interested in social clubs. At the 95% level, what is your estimate of the number of freshmen who would be extremely interested? (HINT: The high and low values of your final confidence interval are proportions. How can proportions be expressed as numbers?)

Expert Solution
To determine

To find:

The confidence interval for the population mean for the specified level.

### Explanation of Solution

Explantion:

Given:

The given information is,

The fraternities and sororities at St. Algebra College have been plagued by declining membership over the past several years and want to know whether the incoming freshman class will be a fertile recruiting ground. Not having enough money to survey all 1600 freshmen, they commission you to survey the interests of a random sample. You find that 35 of your 150 respondents are “extremely” interested in social clubs.

Approach:

The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.

Formula used:

For large samples and given sample proportion, the confidence interval (c.i.) is given by,

c.i.=Ps±Z(Pu(1Pu)N)

Where, Ps is the sample proportion,

Pu is the population proportion,

Z is the Z score determined by the alpha level and,

N is the sample size.

Calculation:

From the given information,

The population proportion is 0.5, sample proportion is 35150.

For 95%, the Z value is given as,

Z(95%)=1.96

For large samples and given sample proportion, the confidence interval (c

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