The population proportion is 0.30. What is the probability that a sample proport

Question

The population proportion is 0.30. What is the probability that a sample proportion will be within plusminus 0.04 of the population proportion for each of the following sample sizes? a. n = 100 b. n = 500 c. What is the advantage of a larger sample size? The president of Doerman Distributors, Inc., believes that 30% of the firm's orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first time customers. a. Assume that the president is correct and p = 0.30. What is the sampling distribution of p for this study? b. What is the probability that the sample proportion p will be between 0.20 and 0.40? c. What is the probability that the sample proportion p will be between 0.25 and 0.35?

Explanation / Answer

Can you post the 6th question separately?

5. pop. prop = p = .30
The probabaility that it will be +/- .04 is?
.04 = Z*sqrt(p *p'/n)

a. n = 100
.04 = Z*sqrt( .3*.7/100)
Z = sqrt(.3*.7/100)/.04 = 1.145
Z = 1.145
The pcumulative from the Z tables is .874
The probability is therefore, 2*(.874-.50) = .748 =~ 75%

b. n = 500
.04 = Z*sqrt( .3*.7/500)
Z = sqrt(.3*.7/500)/.04 = .512
Z = .512
The pcumulative from the Z tables is .695
The probability is therefore, 2*(.695-.50) = .39 =~ 40%

c.

The probability of a larger sample is that you have sweep a smaller area( designated by a smaller probability Area Under Curve of 40% vs. 75% ) to get the same error margin of +/- .04.

In other words, For the same margin of error, a higher sample size means we can find the population proportion inside a smaller area around the mean.

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