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Chapter 7: Q.10 (page 460)

Suppose that you are a student aide in the library and agree to be paid according to the 鈥渞andom pay鈥� 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. The shape of the sampling distribution of xwill be

(a) Normal.

(b) approximately Normal

(c) right-skewed

(d) left-skewed.

(e) symmetric but not Normal.

Short Answer

Expert verified

The Correct answer is (e)

Step by step solution

01

Given Information

Payment for the week if the coin comes up heads=$80

Payment for the week if the coin comes up tails=$40

Number of weeks of work=100

Number of weeks for SRS = 2

02

Explanation

Given the number of the week for SRS is 2.

This means the average amount could be $40for two weeks,$80for two weeks, or $60( $40for one week and $80for the other week).

It is seen that getting $60is twice likely because on the first week $40can be obtained and $80on the second week or vice versa.

Thus, the distribution will be symmetric $60and it will also be normal.

Hence, the correct answer is (e).

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Most popular questions from this chapter

The name for the pattern of values that a statistic takes when we sample repeatedly from the same population is

(a) the bias of the statistic.

(b) the variability of the statistic.

(c) the population distribution.

(d) the distribution of sample data.

(e) the sampling distribution of the statistic.

Mars, Incorporated, says that the mix of colors in its M&M鈥橲庐 Milk Chocolate Candies is 24%blue, 20%orange, 16%green,14%yellow, 13%red, and 13%brown. Assume that the company鈥檚 claim is true. We want to examine the proportion of orange M&M鈥橲 in repeated random samples of 50candies. Which of the graphs that follow could be the approximate sampling distribution of the statistic? Explain your choice

Cold cabin? The Fathom screenshot below shows the results of taking 500SRSs of 10temperature readings from a population distribution that鈥檚 N(50,3)and recording the sample minimum each time.

(a) Describe the approximate sampling distribution.

(b) Suppose that the minimum of an actual sample is 40掳F. What would you conclude about the thermostat manufacturer鈥檚 claim? Explain.

In the language of government statistics, you are 鈥渋n the labor force鈥� if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged 25years and over in a recent year. The table entries are counted by thousands of people.

Unemployment (1.1) Find the unemployment rate for people with each level of education. How does the unemployment rate change with education?

If we take a simple random sample of size n=500from a population of size 5,000,000, the variability of our estimate will be

(a) much less than the variability for a sample of size n=500 from a population of size 50,000,000.

(b) slightly less than the variability for a sample of size n=500from a population of size 50,000,000.

(c) about the same as the variability for a sample of size n=500from a population of size 50,000,000.

(d) slightly greater than the variability for a sample of size n=500from a population of size 50,000,000.

(e) much greater than the variability for a sample of size n=500 from a population of size 50,000,000.
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