(Solved) The countries of Europe report that 46% of the labor force is female. The United Nations wonders if ...

uni67

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The countries of Europe report that 46% of the labor force is female. The United Nations wonders if ...

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor force.

The representatives from the Department of Labor want to estimate a percentage of females in the United States labor force to within ±5%, with 90% confidence. How many employment records should they sample?

Textbook

Stats: Modeling the World

Edition: 4^th

Authors: Bock, Velleman, De Veaux

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kiyomika

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4 years ago

More solutions for this book are available here

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mbowdish

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4 years ago

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor force.

They actually select a random sample of 525 employment records, and find that 229 of the people are females. Create the confidence interval.

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shawntage

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4 years ago

We have a random sample of less than 10% of the employment records, with 229 successes (females) and 296 failures (males), so a Normal model applies.
n = 525,

= 0.436 and

= 0.564, so SE(

) =

= 0.022
margin of error: ME = z* × SE(

) =(1.645)(0.022) = 0.0362.

Confidence interval:

± ME = 0.436 ± 0.0362 or (0.3998, 0.4722)

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mbowdish

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4 years ago

Thanks

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Yeeeee89

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4 years ago

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jzhu11

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4 years ago

We are 90% confident that between 40.0% and 47.2% of the employment records from the United States labor force are for females.

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Suedyso

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4 years ago

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor force.

Should the representatives from the Department of Labor conclude that the percentage of females in their labor force is lower than Europe's rate of 46%? Explain.

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joanamet

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4 years ago

No. Since 46% lies in the confidence interval, (0.3998, 0.4722), it is possible that the percentage of females in the labor force matches Europe's rate of 46% females in the labor force.

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Suedyso

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4 years ago

Helps a lot... Now I'm ready for my quiz

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