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| m102690 | The mean time to earn a bachelor s degree is 5.8 years (Education Planning Resources website, December 5, 2015). Suppose you would like to determine whether the mean time to earn a bachelor s degree is significantly less for students who attend private universities. Data on the time to earn a bachelor s degree for a random sample of 50 individuals who recently earned their bachelor s degrees from private universities are available in the DATAfile named YearsToGrad.
a. State the hypotheses that should be used to test whether the mean time to earn a bachelor s degree is significantly less for students who attend private universities.
b. U se the data in the DATAfile named YearsToGrad to compute the sample mean, the test statistic, and the p-value.
c. Use a 5 .05. What is your conclusion?
d. Repeat the hypothesis test using the critical value approach. |
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| m102691 | The members of a population are numbered 1-4.
a. List the 6 possible samples (without replacement) of size 2 from this population.
b. If an SRS of size 2 is taken from the population, what are the chances of selecting 2 and 3? Explain your answer.
c. Use Table I in Appendix A to obtain an SRS of size 2 from the population. Start at the single-digit number in line number 17 and column number 7, read down the column, up the next, and so on. |
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| m102692 | The members of a population are numbered 1−5.
a. List the 10 possible samples (without replacement) of size 3 from this population.
b. If an SRS of size 3 is taken from the population, what are the chances of selecting 1, 3, and 5? Explain your answer.
c. Use Table I in Appendix A to obtain an SRS of size 3 from the population. Start at the single-digit number in line number 5 and column number 20, read down the column, up the next, and so on. |
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| m102693 | The members of a population are numbered 1-50.
Use Table I in Appendix A to obtain an SRS of size 6 from the population. Start at the two-digit number in line number 10 and column numbers 10−11, read down the column, up the next, and so on. |
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| m102694 | The members of a population are numbered 1-90.
Use Table I in Appendix A to obtain an SRS of size 5 from the population. Start at the two-digit number in line number 15 and column numbers 25−26, read down the column, up the next, and so on. |
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| m102695 | The members of a population have been numbered 1-100. A sample of size 30 is to be taken from the population, using cluster sampling. The clusters are of equal size 10, where cluster #1 consists of the members of the population numbered 1-10, cluster #2 consists of the members of the population numbered 11-20, and so forth.
a. Apply Procedure 1.2 on page 18 to determine the sample (i.e., the numbers corresponding to the members of the population that are included in the sample).
b. Suppose that, in Step 2 of Procedure 1.2, clusters #2, #6, and #9 are selected. Determine the sample. |
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| m102696 | The members of a population have been numbered 1-1000. A sample of size 20 is to be taken from the population, using stratified random sampling with proportional allocation. The strata are of sizes 300, 200, 400, and 100, where stratum #1 consists of the members of the population numbered 1-300, stratum #2 consists of the members of the population numbered 301-500, and so forth.
Determine the sample sizes that will be taken from the strata. |
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| m102697 | The members of a population have been numbered 1-372. A sample of size 5 is to be taken from the population, using systematic random sampling.
a. Apply Procedure 1.1 on page 17 to determine the sample (i.e., the numbers corresponding to the members of the population that are included in the sample).
b. Suppose that, in Step 2 of Procedure 1.1, the random number chosen is 10 (i.e., k = 10). Determine the sample. |
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| m102698 | The members of a population have been numbered 1-50. A sample of size 20 is to be taken from the population, using cluster sampling. The clusters are of equal size 10, where cluster #1 consists of the members of the population numbered 1-10, cluster #2 consists of the members of the population numbered 11-20, and so forth.
a. Apply Procedure 1.2 on page 18 to determine the sample (i.e., the numbers corresponding to the members of the population that are included in the sample).
b. Suppose that, in Step 2 of Procedure 1.2, clusters #1 and #3 are selected. Determine the sample. |
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| m102699 | The members of a population have been numbered 1-500. A sample of size 9 is to be taken from the population, using systematic random sampling.
a. Apply Procedure 1.1 on page 17 to determine the sample (i.e., the numbers corresponding to the members of the population that are included in the sample).
b. Suppose that, in Step 2 of Procedure 1.1, the random number chosen is 48 (i.e., k = 48). Determine the sample. |
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| m102700 | The members of a population have been numbered 1-500. A sample of size 10 is to be taken from the population, using stratified random sampling with proportional allocation. The strata are of sizes 200, 150, and 150, where stratum #1 consists of the members of the population numbered 1-200, stratum #2 consists of the members of the population numbered 201-350, and so forth.
Determine the sample sizes that will be taken from the strata. |
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| m102701 | The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its website. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 12, 1981 to July 8, 2011.
Let X denote the crew size of a randomly selected shuttle mission between the aforementioned dates.
a. What are the possible values of the random variable X?
b. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 7.
c. Find P(X = 4); interpret in terms of percentages.
d. Obtain the probability distribution of X.
e. Construct a probability histogram for X. |
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| m102702 | The National Association of Colleges and Employers (NACE) conducts surveys of salary offers to new college graduates and publishes the results in Salary Survey. The following diagram provides boxplots for the starting annual salaries, in thousands of dollars, obtained from samples of 35 business graduates (top boxplot) and 32 education graduates (bottom boxplot). Use the boxplots to compare the starting salaries of the sampled business graduates and education graduates, paying special attention to center and variation. |
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| m102703 | The National Association of Realtors publishes information on the cost of existing single-family homes in Median Sales Price of Existing Single-Family Homes for Metropolitan Areas. Independent random samples of 10 homes each in Atlantic City and Las Vegas yielded the following data on home prices in thousands of dollars.
At the 5% significance level, can you conclude that the median costs for existing single-family homes differ in Atlantic City and Las Vegas? (Preliminary data analyses suggest that you can reasonably presume that the cost distributions for the two cities have roughly the same shape but that those distributions are right skewed.) |
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| m102704 | The National Center for Education Statistics publishes information about school enrollment in the Digest of Education Statistics. Table 4.17 provides a contingency table for enrollment in public and private schools by level. Frequencies are in thousands of students.
a. How many cells are in this contingency table?
b. How many students are in high school?
c. How many students attend public schools?
d. How many students attend private colleges? |
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| m102705 | The National Center for Health Statistics collects data on health insurance coverage status and coverage type. The following data from the National Health Interview Survey provides the frequency, in millions, of the current health status for persons aged 19-64 and persons aged 65 and over.
a. Obtain a relative-frequency distribution of health status for persons aged 19-64 and a relative-frequency distribution of health status for persons aged 65 and over.
b. Draw a pie chart for both age groups.
c. Compare your pie charts. |
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| m102706 | The National Center for Health Statistics compiles data on injuries and publishes the information in Vital and Health Statistics. A contingency table for injuries in the United States, by circumstance and gender, is as follows. Frequencies are in millions.
a. Find P(C1).
b. Find P(C1 | S2).
c. Are events C1 and S2 independent? Explain your answer.
d. Is the event that an injured person is male independent of the event that an injured person was hurt at home? Explain your answer. |
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| m102707 | The National Center for Health Statistics compiles information on activity limitations. Results are published in Vital and Health Statistics. The data show that 13.6% of males and 14.4% of females have an activity limitation. Are gender and activity limitation statistically independent? Explain your answer. |
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| m102708 | The National Center for Health Statistics publishes information about visits to the dentist in National Health Interview Survey. Here is a joint probability distribution for the length of time (in years) since last visit to a dentist or other dental health professional, by age, for U.S. adults during one year.
For a U.S. adult selected at random, determine the following probabilities and interpret your results in terms of percentages.
a. P(T1)
b. P(not A2)
c. P(A4 & T5)
d. P(T4 | A1)
e. P(A1 | T4) |
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| m102709 | The National Education Association collects data on teacher salaries and publishes results in Estimates of School Statistics Database. Independent samples of 100 secondary school teachers and 125 elementary school teachers yielded the data, in thousands of dollars, on annual salaries as presented on the Weiss Stats site.
a. Obtain histograms, box-plots, and normal probability plots of the two samples.
b. Based on your results from part (a), given the choice between using a pooled t-test or a Mann-Whitney test, which would you choose? Explain your answer.
c. Use both the pooled t-test and the Mann-Whitney test to decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that the average salary of secondary school teachers exceeds that of elementary school teachers. Compare the results of the two tests. |
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