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| m102630 | The English rock band, The Beatles, was formed in Liverpool in 1960. There are 12 studio albums that are considered part of their core catalogue. In the article, "Length of The Beatles Songs" (Chance, Vol. 25, No. 1, pp. 30-33), T. Koyama lists the album title, date of release, and number of songs on each album. Here are the album names and numbers of songs.
Album Number of songs
Please Please Me ........ 14
With the Beatles ......... 14
A Hard Day s Night ..... 13
Beatles for Sale ........... 14
Help! ........................ 14
Rubber Soul .................. 14
Revolver ..................... 14
Sgt. Pepper .............. 13
The Beatles .................. 30
Yellow Submarine ..... 6
Abbey Road ................ 17
Let It Be .................... 12
Find the
a. Mean.
b. Median.
c. Mode(s).
For the mean and the median, round each answer to one more decimal place than that used for the observations |
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| m102631 | The English rock band, The Beatles, was formed in Liverpool in 1960. There are 12 studio albums that are considered part of their core catalogue. In the article, "Length of The Beatles Songs" (Chance, Vol. 25, No. 1, pp. 30-33), T. Koyama lists the album title, date of release, and number of songs on each album. Here are the album names and numbers of songs.
Album Number of songs
Please Please Me .............. 14
With the Beatles .............. 14
A Hard Day s Night .......... 13
Beatles for Sale .............. 14
Help! ......................... 14
Rubber Soul .................. 14
Revolver ..................... 14
Sgt. Pepper ................. 13
The Beatles .................. 30
Yellow Submarine ......... 6
Abbey Road .................. 17
Let It Be ....................... 12
Determine the range and sample standard deviation for each of the data sets. For the sample standard deviation, round each answer to one more decimal place than that used for the observations. |
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| m102632 | The events A1, A2, . . . are mutually exclusive and exhaustive. We have provided P(A1), P(A2), . . . and P(B | A1), P(B | A2), . . . . In each case,
a. Use the rule of total probability to find P(B).
b. Apply Bayes s rule to find P(A1 | B). |
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| m102633 | The factory manager in Exercise 5.43 estimates that each breakdown costs the company $500 in repairs and loss of production. If W is the number of breakdowns in a day, then $500W is the cost of breakdowns for that day.
a. Refer to the probability distribution shown in Exercise 5.43 and determine the probability distribution of the random variable 500W.
b. Determine the mean daily breakdown cost, μ500W, by using your answer from part (a).
c. What is the relationship between μ500W and μW?
d. Find σ500W by using your answer from part (a).
e. What is the apparent relationship between σ500W and σW?
f. The results in parts (c) and (e) hold in general: If W is any random variable and c is a constant,
μcW = cμW and σcW = |c|σW .
Interpret these two equations in words. |
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| m102634 | The family of mammals called Chinchillidae contains the chinchilla and viscachas, which are large South American rodents. The article, "Species Richness and Distribution of Neotropical Rodents, with Conservation Implications" (Mammalia, Vol. 77, Issue 1, pp. 1-19) by G. Amori et al., reports the range sizes of each species of Chinchilladae. There are six species in the Chinchillidae family and the size of each species range, in square kilometers (km2), is given in the following table.
a. Obtain and interpret the population mean range of Chinchilladae species.
b. Obtain and interpret the population standard deviation of the ranges of Chinchilladae species. |
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| m102635 | The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed (2 = 0.18 mm2. An engine inspector took a random sample of 61 fan blades from an engine. She measured each blade and found a sample variance of 0.27 mm2. Using a 0.01 level of signi ficance, is the inspector justi fied in claiming that all the engine fan blades must be replaced? Find a 90% confi dence interval for the population standard deviation
Please provide the following information.
(a) What is the level of signi ficance? State the null and alternate hypotheses.
(b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution?
(c) Find or estimate the P-value of the sample test statistic.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
(e) Interpret your conclusion in the context of the application.
(f) Find the requested confi dence interval for the population variance or population standard deviation. Interpret the results in the context of the application.
. |
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| m102636 | The FBI Standard Survey of Crimes shows that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved (Source: True Odds, by James Walsh, Merrit Publishing). Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetrated by the same criminals. The police are investigating six property crime cases in this district.
(a) What is the probability that none of the crimes will ever be solved?
(b) What is the probability that at least one crime will be solved?
(c) What is the expected number of crimes that will be solved? What is the standard deviation?
(d) How many property crimes n must the police investigate before they can be at least 90% sure of solving one or more cases? |
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| m102637 | The Federal Bureau of Investigation (FBI) compiles information on robbery and property crimes by type and selected characteristic and publishes its findings in Uniform Crime Reports. According to that document, the mean value lost to purse snatching was $468 in 2012. For last year, 12 randomly selected purse-snatching offenses yielded the following values lost, to the nearest dollar.
Use a t-test to decide, at the 5% significance level, whether last year s mean value lost to purse snatching has decreased from the 2012 mean. The mean and standard deviation of the data are $455.0 and $86.8, respectively. |
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| m102638 | The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months.
a. Do the data provide sufficient evidence to conclude that the mean time served for fraud is less than that for firearms offenses? Perform a Mann-Whitney test at a significance level of 0.05.
b. The hypothesis test in part (a) was done in Exercise 10.45 with the pooled t-test. The assumption there is that times served for both offense categories are normally distributed and have equal standard deviations. If that in fact is true, why can you use a Mann- Whitney test to compare the means? Is the pooled t-test or the Mann-Whitney test better in this case? Explain your answers. |
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| m102639 | The Federal Highway Administration compiles information on motor vehicle use around the globe and publishes its findings in Highway Statistics. Following is a contingency table for the number of motor vehicles in use in North American countries, by country and type of vehicle, during one year. Frequencies are in thousands.
a. How many cells are in this contingency table?
b. How many vehicles are Canadian?
c. How many vehicles are motorcycles?
d. How many vehicles are Canadian motorcycles?
e. How many vehicles are either Canadian or motorcycles?
f. How many automobiles are Mexican?
g. How many vehicles are not automobiles? |
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| m102640 | The five top Oklahoma state officials are displayed in Table 1.2 on page 11. Use that table to solve the following problems.
a. List the possible samples of size 1 that can be obtained from the population of five officials.
b. What is the difference between obtaining a simple random sample of size 1 and selecting one official at random?
c. List the possible samples (without replacement) of size 5 that can be obtained from the population of five officials.
d. What is the difference between obtaining a simple random sample of size 5 and taking a census of the five officials? |
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| m102641 | The five top Oklahoma state officials are displayed in Table 1.2 on page 11. Use that table to solve the following problems.
a. List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials.
b. If a simple random sampling procedure is used to obtain a sample of three officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample? |
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| m102642 | The Focus Problem at the beginning of this chapter asks you to use a sign test with a 5% level of signi ficance to test the claim that the overall temperature distribution of Madison, Wisconsin, is different (either way) from that of Juneau, Alaska. The monthly average data (in °F) are as follows.
What is your conclusion?
(a) What is the level of signi ficance? State the null and alternate hypotheses.
(b) Compute the sample test statistic. What is the sampling distribution?
(c) Find the P-value of the sample test statistic.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application. |
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| m102643 | The following cross tabulation shows the average speed of the 25 winners by year of the Daytona 500 automobile race (The 2013 World Almanac).
a. Calculate the row percentages.
b. W hat is the apparent relationship between average winning speed and year? What might be the cause of this apparent relationship? |
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| m102644 | The following data are based on information from the Regis University Psychology Department. In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of three rats was given a reward of one food pellet each time they ran a maze. A second group of three rats was given a reward of one food pellets each time they ran the maze. On day 2, the groups were reversed, so the first group now got one food pellets for running the maze and the second group got only one pellet for running the same maze. The average times in seconds for each rat to run the maze 30 times are shown in the following table.
Do these data indicate that rats receiving larger rewards tend to run the maze in less time? Use a 5% level of signi ficance.
(a) What is the level of signifi cance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
(b) What sampling distribution will you use? What assumptions are you making? Compute the value of the sample test statistic and corresponding t value.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signifi cant at level a?
(e) Interpret your conclusion in the context of the application. |
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| m102645 | The following data are based on information taken from the book Navajo Architecture: Forms, History, Distributions by S. C. Jett and V. E. Spencer (University of Arizona Press). A survey of houses and traditional hogans was made in a number of different regions of the modern Navajo Indian Reservation. The following table is the result of a random sample of eight regions on the Navajo Reservation.
Does this information indicate that the population mean number of inhabited houses is greater than that of hogans on the Navajo Reservation? Use a 5% level of signi ficance.
(a) What is the level of signifi cance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
(b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the value of the sample test statistic and corresponding t value.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signifi cant at level a?
(e) Interpret your conclusion in the context of the application. |
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| m102646 | The following data are paired by date. Let x and y be random variables representing wind direction at 5 A.M. and 5 P.M., respectively (units are degrees on a compass, with 0° representing true north). The readings were taken at seeding level in a cloud seeding experiment.
A random sample of days gave the following information.
Use the sign test with a 5% level of signi ficance to test the claim that the distributions of wind directions at 5 A.M. and 5 P.M. are different. Interpret the results. |
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| m102647 | The following data represent annual percentage returns on Vanguard Total Bond Index for a sequence of recent years. This fund represents nearly all publicly traded U.S. bonds.
(i) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median.
(ii) Test the sequence for randomness about the median. 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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| m102648 | The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (Reference: American Journal of Clinical Nutrition, Vol. 19, pp. 345-351). Note: These data are also available for download at the Companion Sites for this text.
Use six classes? |
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| m102649 | The following data represent petal lengths (in cm) for independent random samples of two species of iris (Reference: E. Anderson, Bulletin American Iris Society). Note: These data are also available for download at the Companion Sites for this text.
Petal length (in cm) of Iris virginica: x1; n1 = 35
Petal length (in cm) of Iris setosa: x2; n2 = 38
(a) Use a calculator with mean and standard deviation keys to verify that x̅1 ( 5.48, s1 ( 0.55, x̅2 ( 1.49, and s2 ( 0.21.
(b) Let (1 be the population mean for x1 and let (2 be the population mean for x2. Find a 99% con fidence interval for (1 - (2.
(c) Interpretation Explain what the con fidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of con fidence, is the population mean petal length of Iris virginica longer than that of Iris setosa .
(d) Check Requirements Which distribution (standard normal or Student s t) did you use? Why? Do you need information about the petal length distributions? Explain. |
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