Sampling variation is caused by

1. (2 points) In a very large population, the distribution of annual income is skewed, with a long right tail. We take a sim- ple random sample of n people from this population and record the n incomes. We expect a histogram of the n incomes in the sample

• A. will resemble a Uniform distribution for all values of n.

• B. will resemble a Uniform distribution provided n is large.

• C. will not resemble a Normal distribution whatever the value of n.

• D. will resemble a Normal distribution for all values of n.

• E. will resemble a Normal distribution provided n is large.

Answer(s) submitted:

• (incorrect)

2. (2 points) For the following problems, select the best re- sponse:

(a) Sampling variation is caused by

• A. changes in a population parameter that cannot be predicted.

• B. systematic errors in our procedure. • C. random selection of a sample. • D. changes in a population parameter from sample to

sample.

(b) A statistic is said to be unbiased if

• A. the survey used to obtain the statistic was designed so as to avoid even the hint of racial or sexual prejudice.

• B. the mean of its sampling distribution is equal to the true value of the parameter being estimated.

• C. both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful.

• D. it is used for only honest purposes. (c) The sampling distribution of a statistic is

• A. the probability that we obtain the statistic in repeated random samples.

• B. the distribution of values taken by a statistic in all possible samples of the same size from the same popu- lation.

• C. the mechanism that determines whether or not ran- domization was effective.

• D. the extent to which the sample results differ system- atically from the truth.

Answer(s) submitted:

• • •

(incorrect)

3. (2 points) The following table provides the starting players of a basketball team and their heights

Player A B C D E Height (in.) 75 77 79 82 85

a. The population mean height of the five players is . b. Find the sample means for samples of size 2.

A, B: x̄ = . A, C: x̄ = . A, D: x̄ = . A, E: x̄ = . B, C: x̄ = . B, D: x̄ = . B, E: x̄ = . C, D: x̄ = . C, E: x̄ = . D, E: x̄ = .

c. Find the mean of all sample means from above: x̄ = .

The answers from parts (a) and (c)

• A. should always be equal • B. are not equal • C. if they are equal it is only a coincidence.

Answer(s) submitted:

• • • • • • • • • • • • •

(incorrect)

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4. (2 points)

What effect does the sample size have on the standard devi- ation of all possible sample means?

• A. It gets smaller as the sample size grows. • B. The sample size has no effect on it. • C. It gets larger as the sample size grows.

Answer(s) submitted: •

(incorrect)

5. (2 points)

Explain why increasing the sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.

• A. The above statement is incorrect, the sample size has no effect on the sampling error.

• B. The larger the sample size, the more closely the pos- sible values of x̄ cluster around the mean of x̄

• C. If the sample size is larger, the possible values of x̄ are farther from the mean of x̄

Answer(s) submitted: •

(incorrect)

6. (2 points) The scores of students on the SAT college en- trance examinations at a certain high school had a normal distri- bution with mean µ = 541.2 and standard deviation σ = 28.4.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 545 or higher? ANSWER:

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x̄, of 35 students? The mean of the sampling distribution for x̄ is: The standard deviation of the sampling distribution for x̄ is:

(c) What z-score corresponds to the mean score x̄ of 545? ANSWER:

(d) What is the probability that the mean score x̄ of these students is 545 or higher? ANSWER:

Answer(s) submitted: • • • •

• (incorrect)

7. (2 points) A study on the length of time a person brushes their teeth is

conducted on a large population of adults. The mean brushing time is µ and the standard deviation is σ. A simple random sam- ple of 100 adults is considered. (NOTE: For the following problems enter: ” GREATER THAN ”, ” EQUAL TO ”, ” LESS THAN ”, or ” NOT ENOUGH INFORMATION ”, without the quotes.)

(a) The mean of the sampling distribution is the mean of the population.

(b) The standard deviation of the sampling distribution is the standard deviation of the population.

Answer(s) submitted: • •

(incorrect)

8. (2 points) Assume that women’s weights are normally distributed with a mean given by µ = 143 lb and a standard deviation given by σ = 29 lb.

(a) If 1 woman is randomly selected, find the probabity that her weight is between 108 lb and 175 lb

(b) If 3 women are randomly selected, find the probability that they have a mean weight between 108 lb and 175 lb

(c) If 64 women are randomly selected, find the probability that they have a mean weight between 108 lb and 175 lb

Answer(s) submitted: • • •

(incorrect)

9. (2 points) A sample of n = 11 observations is drawn from a normal population with µ = 940 and σ = 190. Find each of the following:

A. P(X̄ > 1031) Probability = B. P(X̄ < 836) Probability = C. P(X̄ > 871) Probability = Answer(s) submitted:

• 2

• •

(incorrect)

10. (2 points) A sample of 12 measurements has a mean of 39 and a stan-

dard deviation of 4. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements hav- ing a common value of 39 each.

A. Find the mean of the sample of 14 measurements.

Mean = B. Find the standard deviation of the sample of 14 measure-

ments. Standard Deviation =

Answer(s) submitted:

• •

(incorrect)

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