Question

1) The Wall Street Journal reported that of 33% taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $15,772. Assume that the standard deviation is $2,681. Use z-table.

a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.

n= 30

n= 50

n= 100

n= 400

b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.

A larger sample increases or decreases the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within +196 of ranges from for a sample of size 30 to for a sample of size 400.

2) According to Reader's Digest, 40% of primary care doctors think their patients receive unnecessary medical care. Use z-table.

a. Suppose a sample of 320 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care.

E(p) =

standard deviation p= (to 4 decimals)

b. What is the probability that the sample proportion will be within +0.03 of the population proportion. Round your answer to four decimals.

c. What is the probability that the sample proportion will be within +0.05 of the population proportion. Round your answer to four decimals.

d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why?

The probabilities would - Select your answer -increase/decreaseItem 5 . This is because the increase in the sample size makes the standard error,  ,

Answer 1

1:

In this problem value is missing "within what value of the population mean"

2:

Here we have

a)

The expected value of sample proportion is

The standard error of sample proportion is

b)

The z-score for is

The z-score for is

The required probability is

c)

The z-score for is

The z-score for is

The required probability is

(d)

As the sample size increases, standard error reduces. As the standard error reduces z-scores in part (c) increases. So the probability of part (c) increases as the sample size increases.