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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

The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is 50\( and the standard deviation is 20\). The distribution is not Normal: many households pay a low rate as part of a bundle with phone or television service, but some pay much more for Internet only or for faster connections. 11 A sample survey asks an SRS of 50 households with Internet access how much they pay. Let x-x¯be the mean amount paid.

a. Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds 55 .\(

b. What are the mean and standard deviation of the sampling distribution of x-x¯?

c. What is the shape of the sampling distribution of x-x¯? Justify your answer.

d. Find the probability that the average fee paid by the sample of households exceeds 55 .\)

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

a. reduce the bias of the estimate.

b. increase the bias of the estimate.

c. reduce the variability of the estimate.

d. increase the variability of the estimate.

e. reduce the bias and variability of the estimate.

AP2.20 A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ( \( 500, \) 100, \(25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket:

Which of the following are the mean and standard deviation, respectively, of the winnings?

a. \) 15.00, \( 2900.00

b.\) 15.00, \( 53.85

c. \) 15.00, \( 26.93

d. \) 156.25,\( 53.85

e. \) 156.25, $ 26.93

More sample minimums List all 4possible SRSs of size n=3, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dot plot with the same scale as the dot plot in Exercise 20. How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise 20? What does this indicate about increasing the sample size?

From exercise20:

Car NumberColorAge
1
Red1
2
White5
3
Silver8
4
Red20

Cholesterol Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean μ=188milligrams per deciliter (mg/dl) and standard deviation σ=41mg/dl.

a. Choose an SRS of 100 men from this population. Describe the sampling distribution of x-·x¯.

b. Find the probability that x-x¯estimates μwithin ±3mg/dl. (This is the probability that x-x¯takes a value between 185 and191mg/dl

c. Choose an SRS of 1000 men from this population. Now what is the probability that x- x¯ falls within ±3mg/dl of μ? In what sense is the larger sample "better"?
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