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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.

COLORAGE
RED1
WHITE5
SILVER8
RED20

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.

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 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

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

16.05A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a Normal distribution with mean 16.05 ounces and standard deviation 0.1ounce. Assume that the machine is working properly. If 4 bottles are randomly selected and the number of ounces in each bottle is measured, then there is about a 95%probability that the sample mean will fall in which of the following intervals?

a. 16.05to 16.15ounces

b. 16.00to 16.10ounces

c. 15.95to role="math" localid="1654391534650" 16.15ounces

d. 15.90to 16.20ounces

e. 15.85to 16.25ounces

The mean of this distribution (don鈥檛 try to find it) will be

a. very close to the median.

b. greater than the median.

c. less than the median.

d. You can鈥檛 say, because the distribution isn鈥檛 symmetric.

e. You can鈥檛 say, because the distribution isn鈥檛 Normal.

Tall girls According to the National Center for Health Statistics, the distribution of height for 16-year-old females is modeled well by a Normal density curve with mean 渭=64inches and standard deviation 蟽=2.5inches. Assume this claim is true for the three hundred 16-year-old females at a large high school.

a. Make a graph of the population distribution.

b. Imagine one possible SRS of size 20from this population. Sketch a dotplot of the distribution of sample data.

Suppose we select an SRS of size n=100n=100from a large population having proportion p of successes. Let p鈭�p^be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p鈭�p^?

a. 0.01

b. 0.09

c. 0.85

d. 0.975

e. 0.999
See all solutions

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