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Chapter 7: Q. 69 (page 481)

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 histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

Short Answer

Expert verified

The statement explained by the student is wrong, because the histogram of sample values becomes more Normal as you take larger and larger samples from a population.

Step by step solution

01

Given information

The student made a statement "The histogram of the sample values looks more and more Normal when you take larger and larger samples from a population."

02

According to Question 

It's incorrect because as the sample size grows, the histogram of sample values will take on the shape of the population distribution.

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Most popular questions from this chapter

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

c. in many samples, the values of the statistic are very close to the value of the

parameter.

d. in many samples, the values of the statistic are centered at the value of the parameter.

e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.

Fillings How much do prices vary for filling a cavity? To find out, an insurance company randomly selects 10dental practices in California and asks for the cash (non-insurance) price for this procedure at each practice. The interquartile range is $74.

Detecting gypsy moths The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed with a mean of 0.5 and a standard deviation of 0.7.

a. Explain why it is reasonable to use a Normal distribution to approximate the sampling distribution of x-x¯for SRSs of size 50 .

b. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

c. In a recent month, the mean number of moths in an SRS of size 50 was x-=0.6. x¯=0.6. Based on this result, is there convincing evidence that the moth population is getting larger in this state? Explain your reasoning.

Iced tea On Tuesday, the bottles of Arizona Iced Tea filled in a plant were supposed to contain an average of 20ounces of iced tea. Quality control inspectors selected 50bottles at random from the day’s production. These bottles contained an average of 19.6 ounces of iced tea. Identify the population, the parameter, the sample, and the statistic.

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).
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