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Chapter 7: Q. 20 (page 456)

Sample minimums List all 6possible SRSS of size n=2, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot. Is the sample minimum an unbiased estimator of the population minimum? Explain your answer.

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Short Answer

Expert verified

The required dotplot is and sample proportion not an unbiased estimator of the population proportion.

Step by step solution

01

Given information

We need to find out the proportion of cars in the sample, 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.

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RED1
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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 twoSample minimum
1,2
1
1,3
1
1,4
1
2,3
5
2,4
5
3,4
8

And the required dotplot is,


As the mean of sampling distribution is not equal to population proportion.

So, the sample proportion not an unbiased estimator of the population proportion.

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Most popular questions from this chapter

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

The student newspaper at a large university asks an SRS of 250 undergraduates, "Do you favor eliminating the carnival from the term-end celebration?" All in all, 150 of the 250 are in favor. Suppose that (unknown to you) 55\% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n=250 n=250 from this population, the sampling distribution of the sample proportion p鈭�p^would be

a. exactly Normal with mean 0.55 and standard deviation 0.03.

b. approximately Normal with mean 0.55 and standard deviation 0.03.

c. exactly Normal with mean 0.60 and standard deviation 0.03.

d. approximately Normal with mean 0.60 and standard deviation 0.03.

e. heavily skewed with mean 0.55 and standard deviation 0.03.

Detecting gypsy moths The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed with a mean of 0.5 and a standard deviation of 0.7.

a. Explain why it is reasonable to use a Normal distribution to approximate the sampling distribution of x-x炉for SRSs of size 50 .

b. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

c. In a recent month, the mean number of moths in an SRS of size 50 was x-=0.6. x炉=0.6. Based on this result, is there convincing evidence that the moth population is getting larger in this state? Explain your reasoning.

refer to the following graph. Here is a dotplot of the adult literacy rates in 177 countries in a recent year, according to the United Nations. For example, the lowest literacy rate was 23.6 %, in the African country of Burkina Faso. Mali had the next lowest literacy rate at 24.0 %.

The overall shape of this distribution is

a. clearly skewed to the right.

b. clearly skewed to the left.

c. roughly symmetric.

d. uniform.

e. There is no clear shape.

Iced tea On Tuesday, the bottles of Arizona Iced Tea filled in a plant were supposed to contain an average of 20ounces of iced tea. Quality control inspectors selected 50bottles at random from the day鈥檚 production. These bottles contained an average of 19.6 ounces of iced tea. Identify the population, the parameter, the sample, and the statistic.
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