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Chapter 7: Q. T7.10 (page 438)

Suppose that you are a student aide in the library and agree to be paid according to the "random pay" system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is 80\(. If it comes up tails, your pay for the week is 40\). You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x-x炉. The shape of the sampling distribution of will be

a. Normal.

b. approximately Normal.

c. right-skewed.

d. left-skewed.

e. symmetric but not Normal.

Short Answer

Expert verified

(e). The sample distribution will be symmetric but not normal in shape.

Step by step solution

01

Given Information

The following options are

a. Normal.

b. approximately Normal.

c. right-skewed.

d. left-skewed.

e. symmetric but not Normal.

02

Explanation for correct option

A basic arbitrary sample has a duration of two weeks, with an average duration of two weeks. Because it can get 40$ during the first week, it is twice as likely to get 60$, then 40$, and finally 80$.

As a result, the distribution would be symmetric about $60, but otherwise normal.

As a result, the best solution is (e)

03

Explanation for incorrect option

a. The shape of the sampling distribution of will not be Normal

b. The shape of the sampling distribution of will not be approximately Normal

c. The shape of the sampling distribution of will not be right-skewed.

d. The shape of the sampling distribution of will not be left-skewed .

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Most popular questions from this chapter

Songs on an iPod Refer to Exercise 53 . How many songs would you need to sample if you wanted the standard deviation of the sampling distribution ofx-x炉 to be 10 seconds? Justify your answer.

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.

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13to 16year-olds. The researchers will report the mean xfrom their sample as an estimate of the mean cholesterol level 渭in this population. Explain to someone who knows little about statistics what it means to say that xis an unbiased estimator of 渭.

In a residential neighborhood, the median value of a house is \(200,000. For which of the

following sample sizes is the sample median most likely to be above \)250,000?

(a) n=10n=10

(b) n=50n=50

(c) n=100n=100

(d) n=1000n=1000

(e) Impossible to determine without more information.

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

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

b. Find the probability that x-x炉estimates 渭within 卤3mg/dl. (This is the probability that x-x炉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炉 falls within 卤3mg/dl of 渭? In what sense is the larger sample "better"?
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