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- 1. Multiple Choice
A company has 500 employees and wants to evaluate a proportion using the distribution of sample proportions and normal curve. Under which circumstance will they be able to do this?
n = 80, p = .2
n = 40, p = .2
n = 40, p = .9
n = 30, p = .4
- 2. Multiple ChoiceAt a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?78% is a population and 72% is a sample.72% is a population and 78% is a sample78% is a parameter and 72% is a statistic72% is a parameter and 78% is a statistic
- 3. Multiple Choice
Five estimators for a parameter are being evaluated. The true value of the parameter is 0. Simulations of 100 random samples, each of size n, are drawn from the population. For each simulated sample, the five estimates are computed. The histograms below display the simulated sampling distributions for the five estimators. Which simulated sampling distribution is associated with the best estimator for this parameter?
- 4. Multiple Choice
Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let p̂ be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p̂?
0.01
0.09
0.85
0.978
0.999
- 5. Multiple ChoiceWhat happens to the shape of a sampling distribution of sample means as n increases?It becomes narrower and bimodal.It becomes narrower and more normal.It becomes wider and skewed right.It becomes wider and more normal.
- 6. Multiple Choice
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
- 7. Multiple Choice
Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p?
n = 1,000 and p close to 0
n = 1,000 and p close to 1
n = 1,000 and p close to 1/2
n = 100 and p close to 0
n = 100 and p close to 1/2
- 8. Multiple Choice
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.
- 9. Multiple Choice
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.)
- 10. Multiple Choice
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 ?
- 11. Multiple Choice
In a national study on transportation patterns, 1,000 randomly selected adults will be asked the question: How many trips per week do you make to the grocery store? The sample mean will be computed. Let µ denote the population mean response to the question if everyone in the population is to be asked the question. Is the sample mean x unbiased for estimating µ?
Yes, because for random samples the mean (expected value) of the sample mean x is equal to the population mean µ.
Yes, because with a sample size of 1,000 the standard deviation of the sample mean x is small.
Yes, because the wording of the question is not biased.
No, because the sample mean x does not always equal the population mean µ.
No, because number of trips to the grocery story is not normally distributed so the mean (expected value) of the sample mean x does not equal the population mean µ.
- 12. Multiple Choice
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
- 13. Multiple Choice
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
- 14. Multiple Choice
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.
- 15. Multiple Choice
The histogram below represents data obtained after the census of an entire population was conducted. The sampling distribution of the sample mean based on samples of size 2 for the population was simulated, and a histogram of the results was produced. Which of the following histograms is most likely the histogram of that sampling distribution?
- 16. Multiple ChoiceThe mean weight of potato chip bags is 10.5 ounces with a standard deviation of 3 ounces. A random sample of 40 bags of potato chips is selected. What is the probability that the mean of the sample is less than 10 ounces?P = -1.05P = .1469P = .0202P = .8531
- 17. Multiple ChoiceThe mean distance an OHS student travels to school is 5.6 miles with a standard deviation of 1.7 miles. Mrs. McLemore finds the mean of her 4th period class - a randomly selected sample of 29 students. What is the probability that the mean of her class is more than 6 miles?P = 0.00P = 0.1020P = 0.8980P = 1.27
- 18. Multiple ChoiceIt is estimated that 45% of the senior class will go to prom this year. If you randomly choose 10 seniors and ask them if they are going to prom, could you use the Normal Approximation to predict these results?Yes, both np and nq are greater than 5No, np is less than fiveNo, nq is less than fiveYes, either np or nq are greater than 5
- 19. Multiple ChoiceA z-score tells you...the standard deviation of a sampling distribution.the original raw score on which it is based.if the distribution it comes from is normal.how many standard deviations away from the mean a score lies.
- 20. Multiple Choice
Portly Polls asked 1585 fourth year college students if they still had their original major. According to the colleges, 20% of all fourth year college students still had their original major. What is the probability that Portly Polls' random sample will give a result within 1% of the true value?
68.26%
15.87%
84.13%
52.39%
- 21. Multiple Choice
Random samples of size 11 are selected from a population with mean 33 and standard deviation 6. What is the mean and standard deviation of the sampling distribution?
- 22. Multiple Choice
Portly Polls asked 149 fourth year college students on average, how much they spent for lunch. According to the colleges, the average amount they spent for lunch is N(30,10). Portly Polls got less than $30.4 on average. How likely is this result?
84.02%
68.79%
165.5%
58.37%
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