Question: The Federal Bureau of Investigation (FBI) compiles
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.
> In an issue of Parade Magazine, the editors reported on a national survey on law and order. One question asked of the 2512 U.S. adults who took part was whether they believed that juries “almost always” convict the guilty and free the innocent. Only 578
> Refer to Problem 9. a. Determine a sample size that will ensure a margin of error of at most 0.02 for a 95% confidence interval without making a guess for the observed value of p^. b. Find a 95% confidence interval for p if, for a sample of the size dete
> An international poll of physicians was conducted on the New England Journal of Medicine website asking “Do you believe that the overall medicinal benefits of marijuana outweigh the risks and potential harms?” Identify the: a. specified attribute. b. pop
> Find a 98% confidence interval for the difference between the mean litter sizes of cottonmouths in Florida and Virginia. Interpret your result.
> We have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set, a. determine a frequency distribution. b. obtain a relative-frequency distribution. c. construct a frequency histogram based on
> In the article “The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range” (Journal of Herpetology, Vol. 29, No. 3, pp. 391–398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth. The data
> Refer to Problem 6. Determine a 90% confidence interval for the difference between the mean right-leg strengths of males and females. Interpret your result. Data from Problem 6: In the paper, “Sex Differences in Static Strength and Fatigability in Three
> In the paper, “Sex Differences in Static Strength and Fatigability in Three Different Muscle Groups” (Reasearch Quarterly for Exercise and Sport, Vol. 61(3), pp. 238–242), J. Misner et al. published results of a study on grip and leg strength of males an
> Explain one possible advantage of using a paired sample instead of independent samples.
> Suppose that the variable under consideration is normally distributed on each of the two populations and that you are going to use independent simple random samples to compare the population means. Fill in the blank and explain your answer: Unless you ar
> Regarding the pooled and nonpooled t-procedures, a. what is the difference in assumptions between the two procedures? b. how important is the assumption of independent simple random samples for these procedures? c. how important is the normality assumpti
> The Bureau of Labor Statistics publishes data on weekly earnings of full-time wage and salary workers in Employment and Earnings. Male and female workers were paired according to occupation and experience. Their weekly earnings, in dollars, are provided
> Discuss the basic strategy for comparing the means of two populations based on a simple random paired sample.
> I. Ertugrul et al. conducted a study to determine the association between insulin growth factor 1 (IGF-1) and bone mineral density (BMD) in men over 65 years of age. The researchers published their results in the paper “Relationship Between Insulin-Like
> In the paper, “Drink and Be Merry? Gender, Life Satisfaction, and Alcohol Consumption Among College Students” (Psychology of Addictive Behaviors, Vol. 19, Issue 2, pp. 184–191), J. Murphy et al. examined the impact of alcohol use and alcohol-related prob
> We have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set, a. determine a frequency distribution. b. obtain a relative-frequency distribution. c. construct a frequency histogram based on
> For independent samples, the graphs are for the two samples; for a paired sample, the graphs are for the paired differences. The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the d
> For independent samples, the graphs are for the two samples; for a paired sample, the graphs are for the paired differences. The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the d
> For independent samples, the graphs are for the two samples; for a paired sample, the graphs are for the paired differences. The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the d
> For independent samples, the graphs are for the two samples; for a paired sample, the graphs are for the paired differences. The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the d
> For independent samples, the graphs are for the two samples; for a paired sample, the graphs are for the paired differences. The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the d
> For independent samples, the graphs are for the two samples; for a paired sample, the graphs are for the paired differences. The intent is to employ the sample data to perform a hypothesis test to compare the means of the two populations from which the d
> Find a 90% confidence interval for the difference in the mean lengths of time that ice stays on the two lakes. Interpret your result.
> In the on-line paper “Changes in Lake Ice: Ecosystem Response to Global Change” (Teaching Issues and Experiments in Ecology, tiee.ecoed.net, Vol. 3), R. Bohanan et al. questioned whether there is evidence for global warming in long-term data on changes i
> Discuss the basic strategy for comparing the means of two populations based on independent simple random samples.
> Suppose that you want to conduct a left-tailed hypothesis test at the 5% significance level. How must the critical value be chosen?
> We have presented some quantitative data sets and specified a grouping method for practicing the concepts. For each data set, a. determine a frequency distribution. b. obtain a relative-frequency distribution. c. construct a frequency histogram based on
> True or false: A critical value is considered part of the rejection region.
> Explain the meaning of each term. a. rejection region b. nonrejection region c. critical value(s)
> For a fixed sample size, what happens to the probability of a Type II error if the significance level is decreased from 0.05 to 0.01?
> Two types of incorrect decisions can be made in a hypothesis test: a Type I error and a Type II error. a. Explain the meaning of each type of error. b. Identify the letter used to represent the probability of each type of error. c. If the null hypothesis
> According to the Beer Institute Annual Report, the mean annual consumption of beer per person in the United States is 28.2 gallons (roughly 300 twelve-ounce bottles). A random sample of 300 Missouri residents yielded the annual beer consumption provided
> Body mass index (BMI) is a measure of body fat based on height and weight. According to Dietary Guidelines for Americans, published by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services, for adults, a BMI of greater t
> There are three possible alternative hypotheses in a hypothesis test for a population mean. Identify them and explain when each is used.
> According to Food Consumption, Prices, and Expenditures, published by the U.S. Department of Agriculture, the mean consumption of beef per person in 2011 was 57.5 lb. A sample of 40 people taken this year yielded the data, in pounds, on last year’s beef
> The normal probability plot and stem-and-leaf diagram of the data are shown in Fig; σ is known.
> The normal probability plot and stem-and-leaf diagram of the data are shown in Fig; σ is known.
> Information provided by the World Meteorological Association revealed the following data on the highest recorded temperature for each continent. a. What type of data is presented in the first column of the table? b. What type of data is presented in the
> The normal probability plot and stem-and-leaf diagram of the data are shown in Fig; σ is unknown.
> The normal probability plot and stem-and-leaf diagram of the data are shown in Fig; σ is unknown.
> The normal probability plot and stem-and-leaf diagram of the data are shown in Fig; σ is unknown.
> The normal probability plot and histogram of the data are shown in Fig; σ is unknown.
> The normal probability plot and histogram of the data are shown in Fig; σ is known.
> The normal probability plot and stem-and-leaf diagram of the data are shown in Fig. σ is known.
> The normal probability plot and stem-and-leaf diagram of the data are depicted in Fig. σ is unknown.
> Regarding a hypothesis test: a. What is the procedure, generally, for deciding whether the null hypothesis should be rejected? b. How can the procedure identified in part (a) be made objective and precise?
> The normal probability plot and histogram of the data are depicted in Fig; σ is known.
> College basketball, and particularly the NCAA basketball tournament, is a popular venue for gambling, from novices in office betting pools to high rollers. To encourage uniform betting across teams, Las Vegas oddsmakers assign a point spread to each game
> We have presented a “data scenario.” In each case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best? The carapace lengths, to the nearest hundredth of a millimeter, of a sample of 50 giant tarantulas.
> The following table provides last year’s cheese consumption, in pounds, for 35 randomly selected Americans. a. At the 10% significance level, do the data provide sufficient evidence to conclude that last year’s mean cheese consumption for all Americans h
> Cheese Consumption. The null and alternative hypotheses for the hypothesis test are, respectively, H0: μ = 33 lb (mean has not increased) Ha: μ > 33 lb (mean has increased), where μ is last year’s mean cheese consumption for all Americans. Explain what
> The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed 33 lb of cheese in 2010. Suppose that you want to decide whether last year’s mean cheese consumption is greater than the 2010 mean
> In each part, we have identified a hypothesis-testing procedure for one population mean. State the assumptions required and the test statistic used in each case. a. one-mean t-test b. one-mean z-test
> Discuss the difference between statistical significance and practical significance.
> What is meant when we say that a hypothesis test is a. exact? b. approximately corrects?
> Assess the evidence against the null hypothesis if the P-value of the hypothesis test is 0.062.
> The following statement appeared on a box of Tide laundry detergent: “Individual packages of Tide may weigh slightly more or less than the marked weight due to normal variations incurred with high speed packaging machines, but each day’s production of Ti
> State the general steps of the P-value approach to hypothesis testing.
> We have presented a “data scenario.” In each case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best? The gas mileages, rounded to the nearest number of miles per gallon, of all new car models.
> In each part, we have given the value obtained for the test statistic, z, in a one-mean z-test. We have also specified whether the test is two tailed, left tailed, or right tailed. Determine the P-value in each case and decide whether, at the 5% signific
> How is the P-value of a hypothesis test actually determined?
> Explain why the P-value of a hypothesis test is also referred to as the observed significance level.
> State the decision criterion for a hypothesis test, using the P-value.
> True or false: A P-value of 0.02 provides more evidence against the null hypothesis than a P-value of 0.03. Explain your answer.
> Define the P-value of a hypothesis test.
> State the general steps of the critical-value approach to hypothesis testing.
> The following graph portrays the decision criterion for a one mean z-test, using the critical-value approach to hypothesis testing. The curve in the graph is the normal curve for the test statistic under the assumption that the null hypothesis is true. D
> Determine the critical value(s) for a one-mean z-test at the 1% significance level if the test is a. right tailed. b. left tailed. c. two tailed.
> Explain the meaning of each term. a. null hypothesis b. alternative hypothesis c. test statistic d. significance level
> We have presented a “data scenario.” In each case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best? The number of automobiles per family.
> A variable of a population has a mean of 266 and a standard deviation of 16. Ten observations of this variable have a mean of 262.1 and a sample standard deviation of 20.4. Obtain the observed value of the a. standardized version of x¯. b. studentized v
> Suppose that you plan to apply the one-mean z-interval procedure to obtain a 90% confidence interval for a population mean, μ. You know that σ = 12 and that you are going to use a sample of size 9. a. What will be your margin of error? b. What else do yo
> A confidence interval for a population mean has a margin of error of 10.7. a. Obtain the length of the confidence interval. b. If the mean of the sample is 75.2, determine the confidence interval. c. Express the confidence interval in the form “point est
> Suppose that you intend to find a 95% confidence interval for a population mean by applying the one-mean z-interval procedure to a sample of size 100. a. What would happen to the accuracy of the estimate if you used a sample of size 50 instead but kept t
> Suppose that you have obtained a sample with the intent of performing a particular statistical inference procedure. What should you do before applying the procedure to the sample data? Why?
> If you obtained one thousand 95% confidence intervals for a population mean, μ, roughly how many of the intervals would actually contain μ?
> Must the variable under consideration be normally distributed for you to use the z-interval procedure or t-interval procedure? Explain your answer.
> The rare, booted eagle of western Europe was the focus of a study by S. Suarez et al. to identify optimal nesting habitat for this raptor. According to their paper “Nesting Habitat Selection by Booted Eagles (Hieraaetus pennatus) and Implications for Man
> In the online article “Old Faithful at Yellowstone, a Bimodal Distribution,” D. Howell examined various aspects of the Old Faithful Geyser at Yellowstone National Park. Despite its name, there is considerable variation in both the length of the eruptions
> The U.S. Department of Energy collects fuel economy information on new motor vehicles and publishes its findings in Fuel Economy Guide. The data included are the result of vehicle testing done at the Environmental Protection Agency’s National Vehicle and
> We have presented a “data scenario.” In each case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best? The additional sleep, to the nearest tenth of an hour, obtained by a sample of 100 patients by using a particular br
> The convict surgeonfish is a common tropical reef fish that has been found to delay metamorphosis into adults by extending its larval phase. This delay often leads to enhanced survivorship in the species by increasing the chances of finding suitable habi
> 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 t
> In a Singapore edition of Business Times, diamond pricing was explored. The price of a diamond is based on the diamond’s weight, color, and clarity. A simple random sample of 18 one-half-carat diamonds had the following prices, in dollars. a. Apply the t
> The paper “Correlations between the Intrauterine Metabolic Environment and Blood Pressure in Adolescent Offspring of Diabetic Mothers” (Journal of Pediatrics, Vol. 136, Issue 5, pp. 587–592) by N. Cho et al. presented findings of research on children of
> Refer to Problem 21. a. Find the margin of error, E. b. Explain the meaning of E as far as the accuracy of the estimate is concerned. c. Determine the sample size required to have a margin of error of 0.5 year and a 90% confidence level. d. Find a 90% co
> Researchers M. Dhami et al. discussed how people adjust to prison life in the article “Adaption to Imprisonment” (Criminal Justice and Behavior, Vol. 34, No. 8, pp. 1085–1100). A sample of 712 federally sentenced adult male prisoners had an average sente
> We know that “a 95% confidence interval for the mean age of all U.S. millionaires is from 54.3 years to 62.8 years.” Decide which of the following sentences provide a correct interpretation of the statement in quotes. Justify your answers. a. Ninety-five
> Answer true or false to the following statement and give a reason for your answer: If a 95% confidence interval for a population mean, μ, is from 33.8 to 39.0, the mean of the population must lie somewhere between 33.8 and 39.0.
> Dr. Thomas Stanley of Georgia State University has surveyed millionaires since 1973. Among other information, Stanley obtains estimates for the mean age, μ, of all U.S. millionaires. Suppose that 36 randomly selected U.S. millionaires are the following a
> For a t-curve with df = 18, obtain the t-value and illustrate your results graphically. a. The t-value having area 0.025 to its right b. t0.05 c. The t-value having area 0.10 to its left d. The two t-values that divide the area under the curve into a mid
> We have presented a “data scenario.” In each case, decide which type of grouping (single-value, limit, or cutpoint) is probably the best? The ages of householders, given as a whole number.
> The National Center for Health Statistics published the following data on the leading causes of death in 2010 in National Vital Statistics Reports. Deaths are classified according to the tenth revision of the International Classification of Diseases. Rat
> A random sample of size 13 is taken from a population. A normal probability plot of the sample data shows no outliers but has significant curvature. The population standard deviation is unknown. Decide whether the appropriate method for obtaining the con
> A random sample of size 128 is taken from a population. A normal probability plot of the sample data shows no outliers but has significant curvature. The population standard deviation is known. Decide whether the appropriate method for obtaining the conf
> A random sample of size 20 is taken from a population. A normal probability plot of the sample data shows three outliers but is otherwise roughly linear. Removal of the outliers is questionable. The population standard deviation is unknown. Decide whethe
> A random sample of size 25 is taken from a population. A normal probability plot of the sample data shows three outliers but is otherwise roughly linear. Checking reveals that the outliers are due to recording errors and are really not outliers. The popu
> A random sample of size 50 is taken from a population. A boxplot of the sample data reveals no outliers. The population standard deviation is known. Decide whether the appropriate method for obtaining the confidence interval is the z-interval procedure,
> A random sample of size 17 is taken from a population. A normal probability plot of the sample data is found to be very close to linear (straight line). The population standard deviation is unknown. Decide whether the appropriate method for obtaining the
> The following figure shows the standard normal curve and two t-curves. Which of the two t-curves has the larger degrees of freedom? Explain your answer.
