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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炉

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

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

d. To ensure that x-x炉will be an unbiased estimator of 渭

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炉is not the answer.

b. To ensure that the distribution of x-x炉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炉will be an unbiased estimator of 渭is not the 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.

Finch beaks One dimension of bird beaks is "depth"-the height of the beak where it arises from the bird's head. During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be Normally distributed with mean 渭=9.5鈥�millimeters(mm)and standard deviation 蟽=1.0mm.

a. Choose an SRS of 5 Medium Ground Finches from this population. Describe the sampling distribution of x炉.

b. Find the probability that x炉estimates 渭within 卤0.5mm. (This is the probability that x炉takes a value between 9 and 10 mm.

c. Choose an SRS of 50 Medium Ground Finches from this population. Now what is the probability that x炉falls within 卤0.05mmof 渭? In what sense is the larger sample "better"?

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.

The candy machine Suppose a large candy machine has 45%orange candies, Use Figures 7.11and7.12(page 434) to help answer the following questions.

(a) Would you be surprised if a sample of 25candies from the machine contained 8orange candies (that's 32%orange)? How about 5orange candies ( 20%orange)? Explain.

(b) Which is more surprising getting a sample of 25candies in which 32%are orange or getting a sample of 50candies in which 32%are orange? Explain.

Sample minimums List all 10possible SRSs of size n=3, calculate the minimum quiz score for each sample, and display the sampling distribution of the sample minimum on a dotplot.
See all solutions

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