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Chapter 7: Q. 74 (page 481)

10%Why is it important to check the 10 % condition before calculating probabilities involving localid="1654670795605">x-?

a. To reduce the variability of the sampling distribution of x-x¯

b. To ensure that the distribution of x-x¯is approximately Normal

c. To ensure that we can generalize the results to a larger population

d. To ensure that x-x¯will be an unbiased estimator of μ

e. To ensure that the observations in the sample are close to independent

Short Answer

Expert verified

(e)To ensure that the observations in the sample are close to independent,

Step by step solution

01

Given Information

Check the 10 % condition before calculating probabilities

02

Explanation for correct option

The goal to ensure that the observations in the sample are close to independent is the motivation for testing ten percent conditions first.

As a result, the best solution is (e)

03

Explanation for incorrect option

a. To reduce the variability of the sampling distribution of x-x¯is not the answer.

b. To ensure that the distribution of x-x¯is approximately Norma is not the answer.

c. To ensure that we can generalize the results to a larger population is not the answer.

d. To ensure that x-x¯will be an unbiased estimator of μis not the 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 .\)

A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hour.

a. Without doing any calculations, explain which event is more likely:

  • randomly selecting 1 car entering this interchange during rush hour and finding 2 or more people in the car
  • randomly selecting 35 cars entering this interchange during rush hour and finding an average of 2 or more people in the cars

b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).

c. Calculate the probability of the second event in part (a).

Which of the following statements about the sampling distribution of the sample mean is incorrect?

a. The standard deviation of the sampling distribution will decrease as the sample size increases.

b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean.

c. The sample mean is an unbiased estimator of the population mean.

d. The sampling distribution shows how the sample mean is distributed around the population mean.

e. The sampling distribution shows how the sample is distributed around the sample mean.

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

A study of voting chose 663 registered voters at random shortly after an election. Of these, 72%said they had voted in the election. Election records show that only 56%of registered voters voted in the election. Which of the following statements is true?

a. 72%is a sample; 56%is a population.

b. 72%and 56%are both statistics.

c. 72%is a statistic and 56%is a parameter.

d. 72%is a parameter and 56%is a statistic.

e. 72%and 56%are both parameters.
See all solutions

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