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free/or 0.5$ |
| m102685 | The loss, in millions of dollars, due to a fire in a commercial building is a variable with density curve y = 1 − x/2 for 0 < x < 2, and y = 0 otherwise. Using the fact that the area of a triangle equals one-half its base times its height, we find that the area under this density curve to the left of any number x between 0 and 2 equals x − x2/4.
a. Graph the density curve of this variable.
b. What percentage of losses exceed $1.5 million? |
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| m102686 | The majority party of the U.S. House of Representatives for each year from 1973 to 2003 follow, where D and R represent Democrat and Republican, respectively
D D D D D D D D D D D R R R R R R R
Test the sequence for randomness. Use a = 0.05.
(a) What is the level of signifi cance? State the null and alternate hypotheses.
(b) Find the sample test statistic R, the number of runs.
(c) Find the upper and lower critical values in Table 10 of Appendix II.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application. |
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| m102687 | The manager of Motel 11 has 316 rooms in Palo Alto, California. From observation over a long period of time, she knows that on an average night, 268 rooms will be rented. The long-term standard deviation is 12 rooms. This distribution is approximately mound-shaped and symmetric.
(a) For 10 consecutive nights, the following numbers of rooms were rented each night:
Make a control chart for the number of rooms rented each night, and plot the preceding data on the control chart. Interpretation Looking at the control chart, would you say the number of rooms rented during this 10-night period has been unusually low? unusually high? about what you expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III).
(b) For another 10 consecutive nights, the following numbers of rooms were rented each night:
Make a control chart for the number of rooms rented each night, and plot the preceding data on the control chart. Interpretation Would you say the room occupancy has been high? low? about what you expected? Explain your answer. Identify all out-of-control signals by type (I, II, or III)? |
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| m102688 | The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager s claim.
a. Which form of the hypotheses should be used to test the manager s claim? Explain.
b. What conclusion is appropriate when H0 cannot be rejected?
c. What conclusion is appropriate when H0 can be rejected? |
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| m102689 | The margin of error is also called the maximum error of the estimate. Explain why. |
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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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