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| m102730 | The Professional Golfer s Association of America (PGA) organizes golf tournaments for professional golfers. The following table lists the longest drives, in yards, recorded during a PGA tournament for a random sample of 26 golfers. Use the technology of your choice to decide whether applying the z-interval procedure to these data is reasonable. Explain your answer. |
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| m102731 | The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location II was 200 meters above the discharge point and in midstream. Location III was 50 meters downstream from the discharge point and near the shore. Location IV was 200 meters downstream from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more pollution. Because of the dif ficulty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use an a = 0.05 level of signifi cance. Do we reject or not reject the claim that the quantity of dissolved oxygen does not vary from one location to another?
In the problem, please provide the following information.
(a) What is the level of signifi cance? State the null and alternate hypotheses.
(b) Find SSTOT, SSBET, and SSW and check that SSTOT - SSBET + SSW. Find d.f.BET, d.f.W, MSBET, and MSW. Find the value of the sample test statistic F (F ratio).
What are the degrees of freedom?
(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?
(e) Interpret your conclusion in the context |
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| m102732 | The random variable X is the crew size of a randomly selected shuttle mission between April 12, 1981 and July 8, 2011. Its probability distribution is as follows.
We have provided the probability distributions of the random variables considered in Exercises 5.11-5.15 of Section 5.1. For each exercise, do the following tasks.
a. Find and interpret the mean of the random variable.
b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.5.
c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. |
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| m102733 | The random variable Y is the number of major hurricanes for a randomly selected year between 1851 and 2012. Its probability distribution is as follows.
We have provided the probability distributions of the random variables considered in Exercises 5.11-5.15 of Section 5.1. For each exercise, do the following tasks.
a. Find and interpret the mean of the random variable.
b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.5.
c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. |
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| m102734 | The Recording Industry Association of America (RIAA) reports annual statistics on shipments and revenues. For the year 2012, RIAA reported the following data on physical shipments.
Identify the type of data provided by the information in each of the following columns of the table:
a. First
b. Second
c. Third |
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| m102735 | The report "Addiction Medicine: Closing the Gap between Science and Practice" from the National Center on Addiction and Substance Abuse at Columbia University reveals that addiction treatment is neglected by the medical system in the United States. It shows, in particular, that 16% of Americans have the disease of addiction and that 90% of them receive no form of treatment. Determine the probability that a randomly selected American has the disease of addiction and receives no form of treatment. Interpret your answer in terms of percentages. |
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| m102736 | The reproduction capability of spider mites infected with a bacteria called Cardinium was studied in the article "Cardinium Symbionts Cause Cytoplasmic Incompatibility in Spider Mites" (Heredity, Vol. 98, No. 1, pp. 13-20) by T. Gotoh et al. Infected mites were crossed with mites treated with antibiotics. The following table shows the number of eggs per female for each combination tested. Here we use "A" for antibiotic-treated, "I" for infected, "M" for male, and "F" for female.
At the 10% significance level, do the data provide sufficient evidence to conclude that a difference exists in mean number of eggs among the four combinations?
Perform a Kruskal-Wallis test by using either the critical-value approach or the P-value approach |
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| m102737 | The respiratory disease emphysema, which is most commonly caused by smoking, causes damage to the air sacs in the lungs. According to the National Center for Health Statistics report Data from the National Health Interview Survey, 1.5% of the adult American population suffer from emphysema. Of 100 randomly selected adult Americans, let X denote the number who have emphysema.
a. What are the parameters for the appropriate binomial distribution?
b. What is the parameter for the approximating Poisson distribution?
c. Compute the individual probabilities for the binomial distribution in part (a). Obtain the probabilities until they are zero to four decimal places.
d. Compute the individual probabilities for the Poisson distribution in part (b). Obtain the probabilities until they are zero to four decimal places.
e. Compare the probabilities that you obtained in parts (c) and (d). |
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| m102738 | The Reverend Thomas Bayes (1702-1761) was an English mathematician who discovered an important rule of probability (see Bayes s theorem, Appendix I, part I). A key feature of Bayes s theorem is the formula P (B) = P (B | A) ( P (A) + P (B | Ac) ( P (Ac) Explain why this formula is valid? |
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| m102739 | The rule of thumb for using the normal approximation to the binomial is that both np and n(1 − p) are 5 or greater. Why is this restriction necessary? |
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| m102740 | The same experimental design discussed in Problem 20 was used to test rats trained to climb a sequence of short ladders. Times in seconds for eight rats to perform this task are shown in the following table.
Do these data indicate that rats receiving larger rewards tend to climb the ladder in less time? Use a 5% level of signifi cance.
(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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| m102741 | The sample mean is an unbiased estimator of the population mean. Explain this statement. |
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| m102742 | The sample variance is an unbiased estimator of the population variance when we divide SS by df. What does this mean? |
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| m102743 | The Scottish Executive, Analytical Services Division Transport Statistics, compiles data on motorcycle casualties. During one year, monthly casualties resulting from motorcycle accidents in Scotland for built-up roads and non-built-up roads were as follows.
a. Without doing any calculations, make an educated guess at which of the two data sets, built-up or non-built-up, has the greater variation.
b. Find the range and sample standard deviation of each of the two data sets. Compare your results here to the educated guess that you made in part (a). |
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| m102744 | The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males is affected worldwide, with no ethnic bias.
a. In a sample of 10,000 males, how many would you expect to have Fragile X Syndrome?
b. For a sample of 10,000 males, use the Poisson approximation to the binomial distribution to determine the probability that more than 7 of the males have Fragile X Syndrome; that at most 10 of the males have Fragile X Syndrome. |
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| m102745 | The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males is affected world-wide, with no ethnic bias.
a. In a sample of 10,000 males, how many would you expect to have Fragile X Syndrome?
b. For a sample of 10,000 males, use the normal approximation to the binomial distribution to determine the probability that more than 7 of the males have Fragile X Syndrome; that at most 10 of the males have Fragile X Syndrome.
c. The probabilities in part (b) were obtained in Exercise 5.109 on page 258 by using the Poisson approximation to the binomial distribution. Which estimates of the true binomial probabilities would you expect to be better, the ones using the normal approximation or those using the Poisson approximation? Explain your answer. |
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| m102746 | The sign test can be used whether or not the variable under consideration has a symmetric distribution. If the distribution is in fact symmetric, the Wilcoxon signed-rank test is preferable. Why do you think that is so? |
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| m102747 | The standard direct labor hours allowed is computed as
a. Unit Labor Standard × Actual Output.
b. Unit Labor Standard × Practical Output.
c. Unit Labor Standard × Standard Output.
d. Unit Labor Standard × Normal Output.
e. Unit Labor Standard × Theoretical Output. |
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| m102748 | The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.82, given that a person has tuberculosis. The probability is 0.09 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will
(a) Have tuberculosis and have a positive test?
(b) Not have tuberculosis?
(c) Not have tuberculosis and have a positive test? |
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| m102749 | The study "Intrathecal Sufentanil versus Fentanyl for Lower Limb Surgeries - A Randomized Controlled Trial" (Journal of Anaesthesiology Clinical Pharmacology, Vol. 27, Issue 1, pp. 67-73) by P. Motiani et al. compares two different agents, intrathecal sufentail and fentanyl, used in enhancing the anesthesiology of patients receiving major lower limb surgery.One variable compared between the two agents was the amount of blood loss during the surgery. Based on the study, we will assume that, using fentanyl, the amount of blood loss during major lower limb surgery is normally distributed with mean 283.3 ml and standard deviation 83.3 ml. Find the percentage of patients whose amount of blood loss during major lower limb surgery using fentanyl is
a. Less than 304 ml.
b. Between 221 and 429 ml.
c. More than 450 ml. |
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