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Chapter 7: Q. T7.11 (page 487)

Here are histograms of the values taken by three sample statistics in several hundred samples from the same population. The true value of the population parameter is marked with an arrow on each histogram.

Which statistic would provide the best estimate of the parameter? Justify your answer

Short Answer

Expert verified

The resultant graph is

Step by step solution

01

Given Information

The given graphs

02

Explanation for correct option

The graph shows that the bars are centred around the value and have the least fluctuation (therefore the smallest overall width) (indicated by the arrow).

As a result, histogram A would lead to an excellent parameter estimation.

As a result, the best solution is (A)

03

Explanation for incorrect option

The option (b) and (c) is not the correct answer.

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Most popular questions from this chapter

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x-x炉=810grams. This sample mean is an unbiased estimator of the mean weight 渭 in the population of all ELBW babies, which means that

a. in all possible samples of size 219 from this population, the mean of the values of x-x炉will equal 810 .

b. in all possible samples of size 219 from this population, the mean of the values of x-x炉will equal 渭

c. as we take larger and larger samples from this population, x-x炉will get closer and closer to 渭.

d. in all possible samples of size 219 from this population, the values of x-x炉will have a distribution that is close to Normal.

e. the person measuring the children's weights does so without any error.

More homework Some skeptical Ap庐 Statistics students want to investigate the newspaper's claim in Exercise 11, so they choose an SRS of 100students from the school to interview. In their sample, 45students completed their homework last week. Does this provide convincing evidence that less than 60%of all students at the school completed their assigned homework last week?

a. What is the evidence that less than 60%of all students completed their assigned homework last week?

b. Provide two explanations for the evidence described in part (a).

We used technology to simulate choosing 250SRSs of size n=100n=100from a population of 2000students where 60%completed their assigned homework last week. The dotplot shows pp^the sample proportion of students who completed their assigned homework last week for each of the 250simulated samples.

c. There is one dot on the graph at 0.73. Explain what this value represents.

d. Would it be surprising to get a sample proportion of p=0.45p^=0.45or smaller in an SRS of size 100when p=0.60p=0.60? Justify your answer.

e. Based on your previous answers, is there convincing evidence that less than 60%of all students at the school completed their assigned homework last week? Explain your reasoning.

Unemployment Each month, the Current Population Survey interviews about 60,000 randomly selected U.S. adults. One of their goals is to estimate the national unemployment rate. In October 2016,4.9% of those interviewed were unemployed.

Tall girls? To see if the claim made in Exercise 12is true at their high school, an Ap Statistics class chooses an SRS of twenty 16-year-old females at the school and measures their heights. In their sample, the mean height is 64.7inches. Does this provide convincing evidence that 16-year-old females at this school are taller than 64inches, on average?

a. What is the evidence that the average height of all 16-year-old females at this school is greater than 64inches, on average?

b. Provide two explanations for the evidence described in part (a).

We used technology to simulate choosing 250SRSs of size n=20from a population of three hundred 16-year-old females whose heights follow a Normal distribution with mean localid="1654113150676" 渭=64inches and standard deviation 渭=2.5inches. The dotplot shows x=the sample mean height for each of the 250simulated samples.

c. There is one dot on the graph at 62.5. Explain what this value represents.

d. Would it be surprising to get a sample mean of x=64.7or larger in an SRS of size 20when 渭=64inches and 蟽=2.5inches? Justify your answer.

e. Based on your previous answers, is there convincing evidence that the average height of all 16-year-old females at this school is greater than 64inches? Explain your reasoning.

David鈥檚 iPod has about 10,000songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225seconds and a standard deviation of 60seconds.

a. Describe the shape of the sampling distribution of xfor SRSs of size n=5from the population of songs on David鈥檚 iPod. Justify your answer.

b. Describe the shape of the sampling distribution of x for SRSs of size n=100 from the population of songs on David鈥檚 iPod. Justify your answer.
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