Directions: Draw the normal curve and shade in the specific region. Show formulas used and the substitution. A member of the state legislature wants to determine what fraction of the voters in his district that favors a proposal refunding excess state sales tax revenue to the taxpayers. A random sample of 150 voters in his district shows 80 in his favor in favor. Let p be the population proportion. A. What is the margin of error (E) for this estimate with 95 confidence  B.what sample size does he needs in order to state with 97% confidence that the sample is within .05

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Asked Aug 6, 2019
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Directions: Draw the normal curve and shade in the specific region. Show formulas used and the substitution.

 

A member of the state legislature wants to determine what fraction of the voters in his district that favors a proposal refunding excess state sales tax revenue to the taxpayers. A random sample of 150 voters in his district shows 80 in his favor in favor. Let p be the population proportion.

 

A. What is the margin of error (E) for this estimate with 95 confidence 

 

B.what sample size does he needs in order to state with 97% confidence that the sample is within .05

 

 

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Expert Answer

Step 1

A.

Margin of error (E):

The margin of error for proportion p is given by,

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рхд E Z п х Here, p п

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Step 2

Computing the margin of error for population proportion:

It was found that, 80 voters are in favour out of the 150 voters in his district. That is, n=150 and the sample proportion, p-hat = 0.53 (=80/150). The confidence level is 95%. Therefore, the significance level, α = 0.05 and the z value corresponding to α/2 is 1.96.  The margin of error for population proportion is given by:

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E 1.96,0.53)x (1-0.53) 150 1.96 x 0.041 0.08

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Step 3

B.

Sample Size:

The formula for the sample size is a...

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n p(1-p) E Here Za2 is the critical value at 97% confidence level, p is the population proportion and E is the margin of error

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