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WorksheetsSampling Distributions
Total questions: 16
Worksheet time: 3hrs 40mins
In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?
Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days
Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day
Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day
Approximately normal with mean 5.5 days and standard deviation 2.6 days
Approximately normal with mean 5.5 days and standard deviation 0.26 day
Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?
A sample of size 25 will produce more variability of the estimator than a sample of size 50.
A sample of size 25 will produce less variability of the estimator than a sample of size 50.
A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.
A sample of size 25 will produce a more biased estimator than a sample of size 50.
A sample of size 25 will produce a less biased estimator than a sample of size 50.
According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)
Employees at a large company can earn monthly bonuses. The distribution of monthly bonuses earned by all employees last year has mean 2.3 and standard deviation 1.3. Let z represent the standard normal distribution. If x represents the mean number of monthly bonuses earned last year for a random sample of 40 employees, which of the following calculations will give the approximate probability that x is less than 2 ?
There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
Approximately normal with mean $206,274 and standard deviation $3,788
Approximately normal with mean $206,274 and standard deviation $37,881
Approximately normal with mean $206,274 and standard deviation $520
Strongly right-skewed with mean $206,274 and standard deviation $3,788
Strongly right-skewed with mean $206,274 and standard deviation $37,881
Let X be a random variable that has a skewed distribution with mean µ = 10 and standard deviation σ = 10. Based on random samples of size 400, the sampling distribution of X is
highly skewed with mean 10 and standard deviation 10
highly skewed with mean 10 and standard deviation 5
highly skewed with mean 10 and standard deviation 0.5
approximately normal with mean 10 and standard deviation 10
approximately normal with mean 10 and standard deviation 0.5
A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?
0.1151
0.2743
0.7257
0.8849
Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated.
According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.
The mean of the sampling distribution (for proportions of vaccinated children) would be (a) .
According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.
The standard deviation of the sampling distribution (for proportions of vaccinated children) would be (a) .
(Round answers to three or four decimal places.)
According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.
Which of the following is true concerning the shape of the sampling distribution?
The sampling distribution is normal because n > 30
The sampling distribution is not normal because nq is < 30
The sampling distribution is normal because 10% of 180 is > 10
The sampling distribution is normal because np and nq are both > 10
According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated.
Find the z-score associated with a sample of 180 children in which 162 have been vaccinated.
-1.34
1.34
.0901
.9099
According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated.
Find the probability that a sample of 16 children would have fewer than 14 vaccinated.
-1.34
1.34
.0901
.9099
Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.
The mean of the sampling distribution for average taxi fare where the sample size is 25 is (a) .
Taxi fares in New York City are normally distributed with a mean fare of $22.50 and a standard deviation of $2.20. A tourism agency surveys 25 of its clients who have recently traveled to New York City to determine whether or not this information is accurate.
The standard deviation of the sampling distribution for average taxi fare where the sample size is 25 is (a) .
The mean of the sampling distribution is the same as the mean of the population.
True
False
The standard deviation of a sampling distribution is the same as the standard deviation as the population.
True
False
