Survey of Data Analysis - Chapter 7 Quiz

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is between 15 and 18 is ______. a. 0.8186 b. 0.0228 c. 0.8641 d. 0.8413

A

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What is the probability that fewer than 60% of those surveyed are members of the labor force? a. 0.9706 b. 0.1996 c. 0.7995 d. 0.8400

B

A random sample of size 100 is taken from a population described by the proportion p = 0.60. What are the expected value and the standard error for the sampling distribution of the sample proportion? a. 0.060 and 0.049 b. 0.600 and 0.049 c. 0.006 and 0.0024 d. 0.600 and 0.0024

B The expected value of Pbar is computed as E(Pbar)=p. The standard error of se(Pbar)=√⁢[p⁢( 1⁢ − p⁢ )/n]⁢. E(pbar)=0.60; SE(pbar)=SQRT(0.6*(1-0.6)/100) = 0.049

What is the relationship between the standard deviation of the sample mean and the population standard deviation? a. se(mean)=σ/√(n-1) b. se(mean)=σ/n c. se(mean)=σ/√n d. se(mean)=σ/(n−1)

C

A nursery sells trees of different types and heights. These trees average 40 inches in height with a standard deviation of 13 inches. Suppose that 90 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean? a. 13 b. 4 c. 1.37 d. 2.94

C We call standard deviation the standard error of the sample mean, and it is computed as se(mean)=σ/√n= 13/SQRT(90) = 1.37

Using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met? a. np≤5 and n(1−p)≥5 b. np≥5 and n(1−p)≤5 c. np≤5 and n(1−p)≤5 d. np≥5 and n(1−p)≥5

D

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 95% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that from a sample of 50 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI? a. 0.1469 b. 0.8531 c. 0.0474 d. Cannot be determined

D As a general guideline, the normal distribution approximation is justified when np≥ and n(1−p)≥5 .

According to the 2011 Gallup daily tracking polls (https://www.gallup.com, February 3, 2012), Mississippi is the most conservative U.S. state, with 51.3 percent of its residents identifying themselves as conservative. What is the probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative? a. 0.3974 b. 0.0500 c. 0.5176 d. 0.9013

A Compute P(P<0.5).PP<0.5. Use z table. The appropriate Excel function is =NORM.DIST(50/100,0.513,SQRT(0.513*(1-0.513)/100),TRUE) = 0.3974

According to the 2011 Gallup daily tracking polls (https://www.gallup.com, February 3, 2012), Mississippi is the most conservative U.S. state, with 54.6 percent of its residents identifying themselves as conservative. What is the probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative? a. 0.1778 b. 0.0498 c. 0.6817 d. 0.4846

A Compute P(Pbar<0.5). Use z table. The appropriate Excel function is =NORM.DIST(50/100,0.546,SQRT(0.546*(1-0.546)/100),TRUE) = 0.1778

A random sample of size 49 is taken from a population with mean µ = 15 and standard deviation σ = 5. The probability that the sample mean is greater than 17 is ______. a. 0.0026 b. 0.2764 c. 0.4114 d. 0.6852

A Compute P(X>17). Note that P(Z > z) = 1 − P(Z ≤ z). Use z table. The appropriate Excel function is =1-NORM.DIST(17,15,5/SQRT(49),TRUE) = 0.0021.

According to the central limit theorem, the distribution of the sample means is normal if ________. a. the standard deviation of the population is known b. both the underlying population is normal and the sample size n ≥ 30 are correct c. the sample size n ≥ 30 d. the underlying population is normal

C For any sample size n, the sampling distribution of Xbar is normal if the population X from which the sample is drawn is normally distributed. There is no need for the central limit theorem in these instances. When the underlying distribution is unknown and n ≥ 30, the central limit theorem allows us to assume normality.

If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population? a. For a sample size n > 30, the sampling distribution of the sample mean is normally distributed. b. For a sample size n < 30, the sampling distribution of the sample mean is normally distributed. c. For any sample size n, the sampling distribution of the sample mean is normally distributed. d. For a sample size n < 50, the sampling distribution of the sample mean is normally distributed.

C For any sample size n, the sampling distribution of Xbar is normal if the population X from which the sample is drawn is normally distributed.

The graph below shows the population distribution of variable X with expected value µ. Which of the following statements is TRUE regarding the given sampling distribution of the sample mean, Xbar , with different sample size? a. The green curve has the same sample size as the brown curve. b. The green curve has a larger sample size than the brown curve. c. The green curve is representative of the central limit theorem. d. The green curve has a smaller sample size than the brown curve.

D According to the central limit theorem, the sampling distribution of the sample mean is approximately normal when the sample size gets large enough, as is in the case of the brown curve. Therefore, it can be concluded that the green curve has a smaller sample size than the brown curve.

A random sample of size 100 is taken from a population described by the proportion p = 0.60. The probability that the sample proportion is greater than 0.62 is ______. a. 0.6591 b. 0.4082 c. ≈ 1 d. 0.3415

D Compute P(Pbar>0.62).P(P¯>0.62). Note that P(Z>z)=1−P(Z≤z). Use z table. The appropriate Excel function is =1-NORM.DIST(0.62,0.6,SQRT(0.6*0.4/100),TRUE) = 0.3415

Suppose the average math SAT score for students enrolled at a local community college is 490.4 with a standard deviation of 63.7. A random sample of 49 students has been selected. The standard error of the mean for this sample is ______. a. 10.6 b. 28.4 c. 63.7 d. 9.1

D The standard deviation of Xbar (or the standard error of the sample mean) is calculated as the positive square root of the variance. It is computed as se(Xbar)=σ/√n=63.7/SQRT(49) = 9.1.

A nursery sells trees of different types and heights. These trees average 50 inches in height with a standard deviation of 12 inches. Suppose that 80 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean? a. 12 b. 2.91 c. 3 d. 1.34

D We call standard deviation the standard error of the sample mean, and it is computed as se(mean)=σ/√n= 12/SQRT(80) = 1.34