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| m102930 | Why do two normal distributions that have equal standard deviations have the same shape? |
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| m102931 | Why is obtaining the mean and standard deviation of x̅ a first step in approximating the sampling distribution of the sample mean by a normal distribution? |
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| m102932 | Why is the basic counting rule (BCR) often referred to as the multiplication rule? |
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| m102933 | Why is the phrase "goodness of fit" used to describe the type of hypothesis test considered in this section? |
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| m102934 | Why is the variance not meaningful to analyze ordinal scale data? |
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| m102935 | Why should you generally expect some error when estimating a parameter (e.g., a population mean) by a statistic (e.g., a sample mean)? What is this kind of error called? |
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| m102936 | Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179-188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows:
Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of signifi cance?
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 of the application.
(f) Make a summary table for your ANOVA test. |
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| m102937 | Wildfires are uncontrolled fires that usually spread quickly and are common in wilderness areas that have long and dry summers. The National Interagency Fire Center reports statistics on wildfires on their website www.nifc.gov. The following data lists the size, in thousands of acres, of a sample of 14 large (at least 100,000 acres) wildfires.
Use the technology of your choice to decide whether applying the one-mean t-interval procedure to these data is reasonable. Justify your answer. |
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| m102938 | Wilfley and colleagues (2008) tested whether the antiobesity drug sibutramine would be an effective treatment for people with binge eating disorder. They measured the frequency of binge eating every 2 weeks for 24 weeks during treatment. The following table lists a portion of the data similar to results reported by the authors for the frequency of binge eating over the first 8 weeks of the drug treatment.
(a) Complete the F table and make a decision to retain or reject the null hypothesis.
(b) Use the Bonferroni procedure to make the post hoc test. In which week do we first see significant differences compared to baseline? |
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| m102939 | Wind Mountain is an archaeological study area located in southwestern New Mexico. Pot sherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations (Source: Based on information from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre, University of New Mexico Press).
Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance.
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 of the application.
(f) Make a summary table for your ANOVA test. |
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| m102940 | Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a pro fit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a pro fit in either of the fi rst 2 years. The accounting of fice at Wing Foot provided the following information: 65% of all Wing Foot stores show a pro fit the fi rst year; 71% of all Wing Foot stores show a pro fit the second year (this includes stores that did not show a profi t the fi rst year); however, 87% of Wing Foot stores that showed a pro fit the fi rst year also showed a pro fit the second year. Compute the following:
(a) P (A)
(b) P (B)
(c) P (B | A)
(d) P (A and B)
(e) P (A or B)
(f) What is the probability that a new Wing Foot store will not be closed after 2 years? What is the probability that a new Wing Foot store will be closed after 2 years? |
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| m102941 | With an ever-increasing world population, grain yields are extremely important. A random sample of 16 large grain producing regions in the world gave the following information about grain production (in kg/hectare)
Does this information indicate that modern grain production is higher? Use a 5% level of signifi cance.
(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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| m102942 | With regard to the use of a Poisson distribution to approximate binomial probabilities, on page 254 we stated that "As you might expect, the appropriate Poisson distribution is the one whose mean is the same as that of the binomial distribution. . . ." Explain why you might expect this result. |
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| m102943 | Without consulting Table II, explain why the area under the standard normal curve that lies to the right of 0 is 0.5? |
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| m102944 | Witt and Schrodt (2006) tested the relationship between nonverbal immediacy (behaviors that enhance closeness and nonverbal interaction with others) and technology. They tested whether teacher nonverbal immediacy (high, low) in classes with different levels of technology use (none, minimal, moderate, complete) would influence student perceptions of the teacher. They computed a 4 × 2 ANOVA to analyze the data. The table lists the cell means at each level of the two factors.
(a) Graph the cell means.
(b) Is a possible interaction evident? Explain. |
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| m102945 | Wolf packs tend to be large extended family groups that have a well-defi ned hunting territory. Wolves not in the pack are driven out of the territory or killed. In ecologically similar regions, is the size of an extended wolf pack related to size of hunting region? Using radio collars on wolves, the size of the hunting region can be estimated for a given pack of wolves. Let x represent the number of wolves in an extended pack and y represent the size of the hunting region in km2/1000. From Denali National Park we have the following data.
Reference: The Wolves of Denali by Mech, Adams, Meler, Burch, and Dale. University of Minnesota Press.
(a) Verify that Σx = 252. Σy = 59.86. Σx2 = 16,894. Σy2 = 787.0194. Σxv = 3527.87, and r ≈ 0.9405.
(b) Use a 1% level of significance to test the claim ρ > 0.
(c) Verify that Se ≈ 1.6453, a ≈ 5.8309.and b ≈ 0.l2l85.
(d) Find the predicted size of the hunting region for an extended pack of 42 wolves.
(e) Find an 85% confidence interval for your prediction of part (d).
(1) Use a 1% level of significance to test the claim that β > 0.
(g) Find a 95% confidence interval for and interpret its meaning in terms of territory size per wolf. |
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| m102946 | Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then ( ( 7500 and ( ( 1750 (Reference: Diagnostic Tests with Nursing Applications, S. Loeb).
A random sample of n = 50 workers from the toxic cleanup site were given a blood test that showed x̅ = 6820. What is the probability that, for healthy adults, x̅ will be this low or lower?
(a) How does the central limit theorem apply? Explain.
(b) Compute P(x̅ ( 6820).
(c) Interpretation Based on your answer to part (b), would you recommend that additional facts be obtained, or would you recommend that the workers concerns be dismissed? Explain. |
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| m102947 | Write a brief but complete essay in which you describe the probability distributions you have studied so far. Which apply to discrete random variables? Which apply to continuous random variables? Under what conditions can the binomial distribution be approximated by the normal? by the Poisson? |
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| m102948 | Yahoo Finance reported the beta value for Coca-Cola was .82 (Yahoo Finance website, June 30, 2016). Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock, and the independent variable is the total return for the stock market, such as the return of the S&P 500. The slope of this regression equation is referred to as the stock s beta. Many financial analysts prefer to measure the risk of a stock by computing the stock s beta value.
The data contained in the DATAfile named CocaCola show the monthly percentage returns for the S&P 500 and the Coca-Cola Company for August 2015 to May 2016.
a. Develop a scatter diagram with the S&P % Return as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the returns of the S&P 500 and those of the Coca-Cola Company?
c. Develop the least squares estimated regression equation.
d. Provide an interpretation for the slope of the estimated equation (that is, the beta).
e. Is your beta estimate close to .82? If not, why might your estimate be different? |
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| m102949 | Yellowstone Park Medical Services (YPMS) provides emergency health care for park visitors. Such health care includes treatment for everything from indigestion and sunburn to more serious injuries. A recent issue of Yellowstone Today (National Park Service Publication) indicated that the average number of visitors treated each day by YPMS is 21.7. The estimated standard deviation is 4.2 (summer data). The distribution of numbers treated is approximately mound-shaped and symmetric.
(a) For a 10-day summer period, the following data show the number of visitors treated each day by YPMS:
Make a control chart for the daily number of visitors treated by YPMS, and plot the data on the control chart. Do the data indicate that the number of visitors treated by YPMS is "in control"? Explain your answer.
(b) For another 10-day summer period, the following data were obtained:
Make a control chart, and plot the data on the chart. Interpretation Do the data indicate that the number of visitors treated by YPMS is "in control" or "out of control"? Explain your answer. Identify all out-of-control signals by type (I, II, or III). If you were the park superintendent, do you think YPMS might need some (temporary) extra help? Explain. |
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