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StatisticsEssentials Of StatisticsS 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? )BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 6, Problem 6.17P

Textbook Problem

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*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.

**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,

Where,

*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

For 95%, the *Z* value is given as,

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

Essentials Of Statistics

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