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1. In state A, 23% of the people drink coffee. In state B, 37% of the...

1.

In state A, 23% of the people drink coffee. In state B, 37% of the people drink coffee.

We take a random sample of 50 from state A, and 60 from state B, and find the sample proportions spA and spB (spA is the sample proportion of those who drink coffee from state A, which in the notation of the textbook would be p1)

What is the mean of spA - spB? (write it as a decimal fraction, not a percentage; provide two decimal places)

2.

In state A, 19% of the people drink coffee. In state B, 32% of the people drink coffee.

We take a random sample of 50 from state A, and 60 from state B, and find the sample proportions spA and spB (spA is the sample proportion of those who drink coffee from state A, which in the notation of the textbook would be  p1 )

What is the standard deviation of spA - spB? (write it as a decimal fraction, not a percentage; provide two decimal places)

3.

We are comparing the population between two states regarding the proportion of tax payers who itemize deductions. In state 1, from a random sample of 250, 180 were seen to itemize deductions.  In state 2, from a random sample of 300, 90 were seen to itemize deductions.

Compute the pooled proportion of tax payers who itemize deductions. (provide  two decimal places)

4.

We are comparing the population between two states regarding the proportion of tax payers who itemize deductions. In state 1, from a random sample of 250, 180 were seen to itemize deductions.  In state 2, from a random sample of 300, 90 were seen to itemize deductions.  

The hypothesis would be H0: p1 = p2; H1: p1 is not equal to p2.

Compute the appropriate test statistic. (provide  two decimal places)

Math   Statistics-And-Probability   
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Answer #1

Hi, since questions 1 and 2 are related, I am helping you with these two questions ...

(1) The distribution of the difference between two sample proportions, , is approximately normal.

Mean of (spA - spB) = p1 - p2 = 0.23 - 0.37 = -0.14

(2) The distribution of the difference between two sample proportions, , is approximately normal.

Standard deviation of (spA - spB) = √[(p1 q1/n1) + (p2 q2/n2)] = √[(0.19 * 0.81/50) + (0.32 * 0.68/60)] = 0.082

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