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Chapter 7: Q. T7.6 (page 486)

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x¯. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x¯will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

b. 80

c. 320

d. 640

e. There is not enough information to determine the sample size.

Short Answer

Expert verified

(d). The sample size should the researcher is 640

Step by step solution

01

Given Information

Initially, a researcher intends to collect an SRS of size 160 from a specific demographic.

02

Explanation for correct option

The initial sample size was 160 people.

σx¯=σn

to reduce the standard deviation by half

σx¯2=12×σn=σ2n=σ22n=σ4n

In the equation of the standard deviation, the sample size n is replaced with 4 n, implying that the sample quadruples in size. n was the initial sample size. The sample with a standard deviation half as large

4n=4(160)=640

Hence, the correct option is (d)

03

Explanation for incorrect option

a. 40 is not the answer.

b. 80 is not the answer.

c. 320 is not the answer.

e. There is not enough information to determine the sample size is not the answer.

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Most popular questions from this chapter

In a certain large population of adults, the distribution of IQ scores is strongly left skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. For SRSs of size 200, the distribution of sample mean IQ score is

a. left-skewed with mean 122 and standard deviation 0.35.

b. exactly Normal with mean 122 and standard deviation 5.

c. exactly Normal with mean 122 and standard deviation 0.35.

d. approximately Normal with mean 122 and standard deviation 5.

e. approximately Normal with mean 122 and standard deviation 0.35.

The probability distribution for the number of heads in four tosses of a coin is given by

Number of heads
01234
Probability
0.06250.2500
0.3750
0.2500
0.0625

The probability of getting at least one tail in four tosses of a coin is

a. 0.2500

b. 0.3125

c. 0.6875

d. 0.9375

e. 0.0625


On one episode of his show, a radio show host encouraged his listeners to visit his website and vote in a poll about proposed tax increases. Of the 4821 people who vote, 4277 are against the proposed increases. To which of the following populations should the results of this poll be generalized?

a. All people who have ever listened to this show

b. All people who listened to this episode of the show

c. All people who visited the show host's website

d. All people who voted in the poll

e. All people who voted against the proposed increases

Making auto parts Refer to Exercise 54 . How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of x-x¯to be 0.0005mm ? Justify your answer.

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

c. in many samples, the values of the statistic are very close to the value of the

parameter.

d. in many samples, the values of the statistic are centered at the value of the parameter.

e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.
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