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Chapter 7: Q. 19 (page 456)

Sample proportions List all 6possible SRSS of size n=2, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot. Is the sample proportion an unbiased estimator of the population proportion? Explain your answer.

COLORAGE
RED1
WHITE5
SILVER8
RED20

Short Answer

Expert verified

The required dotplot isand sample proportion an unbiased estimator of the population proportion.

Step by step solution

01

Given information

We need to find out the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot and whether the sample proportion is an unbiased estimator of the population proportion or not.

COLORAGE
RED1
WHITE5
SILVER8
RED20
02

Explanation

We know that

The sample proportion of all the red cars is equal to half of the no. of red cars in the sample.

Sample of size twoNumber of red carsProportion of red cars
1,2
10.5
1,3
10.5
1,4
10.5
2,3
00
2,4
10.5
3,4
2
1

And the required dotplot is,


As the mean of sampling distribution is equal to population proportion.

So, the sample proportion an unbiased estimator of the population proportion.

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Most popular questions from this chapter

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which 65 or fewer own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

a. (10065)(0.71)65(0.29)3510065(0.71)65(0.29)35

b. (10065)(0.29)65(0.71)3510065(0.29)65(0.71)35

c.

P(z≤0.65-0.71(0.71)(0.29)100)Pz≤0.65-0.71(0.71)(0.29)100

d.P(z≤0.65-0.71(0.65)(0.35)100)Pz≤0.65-0.71(0.65)(0.35)100

e.P(z≤0.65-0.71(0.71)(0.29)100)Pz≤0.65-0.71(0.71)(0.29)100

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