Question

1. Which of the following statements best describes a sampling distribution?

Select one:

a. It is the distribution of the values of a variable in the population from which the sample is taken

b. It is the distribution of the values of a statistic that resembles the normal distribution when the sample size is large

c. It is the distribution of the values of a statistic calculated from 1000 simple random samples displayed in a histogram.

d. It is the distribution of the values of a particular variable that are observed in a random sample.

2. The weight of extra-large egg has a Normal distribution with a mean of 3 oz and a standard deviation of 0.1 oz.

What is the sampling distribution of the mean weight of extra-large egg (i.e., the distribution of the sample mean weight of an egg in a randomly selected carton of a dozen eggs (i.e., 12 eggs))?     

Select one:

a. N(12,1)

b. N(3, 0.1)

c. N(3, 0.03)

d. N(3, 0.2)

3. The manager at a movie theater would like to estimate the true mean amount of money spent by customers on popcorn only. He selects a simple random sample of 26 receipts and calculates a 92% confidence interval for true mean to be ($12.45, $23.32). The confidence interval can be interpreted to mean that, in the long run,                   

Select one:

a. 92% of all customers who buy popcorn spend between $12.45 and $23.22

b. 92% of similarly constructed intervals would contain the population mean

c. 92% of similarly constructed intervals would contain the sample mean

4. A population variable has a distribution with mean µ = 25 and variance σ² is 256. From this population a simple random sample of n observations is to be selected and the mean of the sample values calculated. If the population variable is known to be Normally distributed and the sample size is to be n = 25, what is the probability that the sample mean will be between 20.5 and 31.50, i.e., P(20.5 ≤ x-bar ≤ 31.5)?

5. Since confidence intervals are based on the sampling distribution of the sample mean, it is possible to form confidence intervals when sampling from slightly skewed distributions due to the central limit theorem

Select one:

True

False

6. The heights of a simple random sample of 200 male high school sophomores in a midwestern state are measured. The sample mean (x-bar) is 70 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation is 5 inches.    

What is a 99% confidence interval for the population mean μ?

Select one:

a. (59.46, 72.94)

b. (69.09, 70.91)

c. (65.67, 66.73)

d. (58.16, 74.24)

7. The heights of a simple random sample of 200 male high school sophomores in a midwestern state are measured. The sample mean (x-bar) is 70 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of σ is 5 inches.

Suppose the heights of a simple random sample of 100 male sophomores were measured instead of 200. Which of the following statements is true?  

Select one:

a. The margin of error for the 95% confidence interval would decrease

b. The margin of error for the 95% confidence interval would increase

c. The standard deviation would decrease

Answer 1

1. Option(b). It is the distribution of values of statistic that resembles the normal distribution when the sample size is large.

2. Option(c). Explanation is attached below.

3. Option(a). 92% of all customers who buy popcorn would spend between $12.45 and $23.22

4. Solved below.

5. False. For constructing confidence intervals for non-normal data, bootstrap methods are used.

6. Option(b). Solved below.

7. Option (b). The margin of error for 95% confidence interval would increase. ( Margin of error increases with decrease in sample size.)