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Elementary Statistics 8th Edition Neil A. Weiss - Solutions

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.
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.Determine the a. Rejection region. b.
State the general steps of the critical-value approach to hypothesis testing.
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% significance level, the data provide sufficient
State the general steps of the P-value approach to hypothesis testing.
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 Tide will average slightly above the marked
What is meant when we say that a hypothesis test is a. Exact? b. Approximately correct?
Discuss the difference between statistical significance and practical significance.
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
The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed 30.0 lb of cheese in 2001. Cheese consumption has increased steadily since 1960, when the average American ate only 8.3 lb of cheese annually. Suppose that you want to decide
The null and alternative hypotheses for the hypothesis test in Problem 24 are, respectively, H0: μ = 30.0 lb (mean has not increased) Ha: μ > 30.0 lb (mean has increased), where μ is last year's mean cheese consumption for all Americans. Explain what each of the following would mean. a. Type I
Refer to Problem 24. 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 has increased over the
The Federal Bureau of Investigation (FBI) compiles information on robbery and property crimes by type and selected characteristic and publishes its findings in Population-at-Risk Rates and Selected Crime Indicators. According to that document, the mean value lost to purse snatching was $417 in
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. The point spread is the oddsmakers'
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?
There are three possible alternative hypotheses in a hypothesis test for a population mean. Identify them, and explain when each is used.
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 is in fact true, only one type of error is
Explain the meaning of each term. a. Rejection region b. Nonrejection region c. Critical value(s)
An issue of USA TODAY discussed the amounts spent by teens and adults at shopping malls. Suppose that we want to perform a hypothesis test to decide whether the mean amount spent by teens is less than the mean amount spent by adults. a. Identify the variable. b. Identify the two populations. c.
In the paper "An Analysis of Factors That Contribute to the Efficacy of Hypnotic Analgesia" (Journal of Abnormal Psychology, Vol. 96, No. 1, pp. 46-51), D. Price and J. Barber examined the effects of hypnosis on pain. They measured response to pain using a visual analogue scale (VAS), in
In the paper "Housing Values Near New Sporting Stadiums" (Land Economics, Vol. 81, Issue 3, pp. 379-395), C. Tu examined the effects of construction of new sports stadiums on home values. Suppose that you want to use a paired sample to decide whether construction of new sports stadiums affects the
In the article "Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy" (American Industrial Hygiene Association Journal, Vol. 63, pp. 756-761), I. Moa et al. reported on determining fiber density by two different methods. The fiber density of 10 samples with varying
The null hypothesis is H0: μ1 = μ2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required hypothesis test at the 10% significance
Ha: Î¼1The null hypothesis is H0: Î¼1 = Î¼2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required
Ha: Î¼1 > Î¼2The null hypothesis is H0: Î¼1 = Î¼2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform
Ha: Î¼1 ‰ Î¼2The null hypothesis is H0: Î¼1 = Î¼2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test
Ha: Î¼1The null hypothesis is H0: Î¼1 = Î¼2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform the required
Ha: Î¼1 > Î¼2The null hypothesis is H0: Î¼1 = Î¼2 and the alternative hypothesis is as specified. We have provided data from a simple random paired sample from the two populations under consideration. In each case, use the paired t-test to perform
Charles Darwin, author of Origin of Species, investigated the effect of cross-fertilization on the heights of plants. In one study he planted 15 pairs of Zea mays plants. Each pair consisted of one cross-fertilized plant and one self-fertilized plant grown in the same pot. The following table gives
Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey, Summary of Travel Trends. A hypothesis test is to be performed to decide whether a difference exists in last year's mean VMT for
In 1908, W. S. Gosset published "The Probable Error of a Mean" (Biometrika, Vol. 6, pp. 1-25). In this pioneering paper, published under the pseudonym "Student," he introduced what later became known as Student's t-distribution. Gosset used the following data set, which gives the additional sleep
Anorexia nervosa is a serious eating disorder, particularly among young women. The following data provide the weights, in pounds, of 17 anorexic young women before and after receiving a family therapy treatment for anorexia nervosa.Does family therapy appear to be effective in helping anorexic
R. Stichler et al. compared two methods of measuring treadwear in their paper "Measurement of Treadwear of Commercial Tires" (Rubber Age, Vol. 73:2). Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The following are the data, in
Glaucoma is a leading cause of blindness in the United States. N. Ehlers measured the corneal thickness of eight patients who had glaucoma in one eye but not in the other. The results of the study were published as the paper "On Corneal Thickness and Intraocular Pressure, II" (Acta Opthalmologica,
V. Tangpricha et al. conducted a study to determine whether fortifying orange juice with vitamin D would increase serum 25-hydroxyvitamin D [25(OH)D] concentration in the blood. The researchers reported their findings in the paper "Fortification of Orange Juice with Vitamin D: A Novel Approach for
Refer to Exercise 10.109.a. Determine a 95% confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized Zea mays. b. Repeat part (a) for a 99% confidence level.
Refer to Exercise 10.110.a. Determine a 90% confidence interval for the additional sleep that would be obtained, on average, by using laevohysocyamine hydrobromide.b. Repeat part (a) for a 98% confidence level.
Refer to Exercise 10.111 and find a 90% confidence interval for the weight gain that would be obtained, on average, by using the family therapy treatment.
Refer to Exercise 10.112 and find a 95% confidence interval for the mean difference in measurement by the weight and groove methods.
Refer to Exercise 10.113 and obtain an 80% confidence interval for the difference between the mean corneal thickness of normal eyes and that of eyes with glaucoma.
In the introduction to this chapter, we mentioned comparing the mean age of buyers of new domestic cars to the mean age of buyers of new imported cars. Suppose that we want to perform a hypothesis test to decide whether the mean age of buyers of new domestic cars is greater than the mean age of
Refer to Exercise 10.114 and obtain a 98% confidence interval for the mean increase of the serum 25(OH)D concentration after 12 weeks of drinking fortified orange juice.
To assess the effects of two different strains of the tobacco mosaic virus, W. Youden and H. Beale randomly selected eight tobacco leaves. half of each leaf was subjected to one of the strains of tobacco mosaic virus and the other half to the other strain. The researchers then counted the number of
The makers of the MAGNETIZER Engine Energizer System (EES) claim that it improves gas mileage and reduces emissions in automobiles by using magnetic free energy to increase the amount of oxygen in the fuel for greater combustion efficiency. Following are test results, performed under international
In the article "Improved Outcome for Children With Disseminated Adenoviral Infection Following Allogeneic Stem Cell Transplantation" (British Journal of haematology, Vol. 130, Issue 4, p. 595), B. Kampmann et al. examined children who received stem cell transplants and subsequently became infected
The American Association of University Professors (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. In Example 10.3 on page 399, we performed a hypothesis test based on independent samples to decide
In the Statistics Norway on-line article "The Times They Are a Changing," J. Kristiansen discussed the changes in age at the time of marriage in Norway. The ages, in years, at the time of marriage for 75 Norwegian couples are presented on the WeissStats CD. Use the technology of your choice to do
In the document "Peak Discharge from Unlogged and Logged Watersheds," J. Jones and G. Grant compiled (paired) data on peak discharge from storms in two watersheds, one unlogged and one logged (100% clear-cut). If there is an effect due to clear-cutting, one would expect that the runoff would be
Explain exactly how a paired t-test can be formulated as a one-mean t-test.
This exercise shows what can happen when a hypothesis-testing procedure designed for use with independent samples is applied to perform a hypothesis test on a paired sample. The gas mileages, in miles per gallon (mpg), of 10 randomly selected cars, both with and without a new gasoline additive, are
An Arizona State University professor, R. Jacobowitz, Ph.D., in consultation with G. Vishteh, M.D., and other neurosurgeons obtained data on operative times, in minutes, for both a dynamic system (Z-plate) and a static system (ALPS plate). They wanted to perform a hypothesis test to decide whether
Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the paired t-test, the paired Wilcoxon signed-rank test, or neither of these tests, if preliminary data analyses of the sample of paired
Suppose that you want to perform a hypothesis test to compare the means of two populations, using a paired sample. For each part, decide whether you would use the paired t-test, the paired Wilcoxon signed-rank test, or neither of these tests, if preliminary data analyses of the sample of paired
D. Cristol et al. published results of their studies of two subspecies of dark-eyed juncos in the paper "Migratory Dark-Eyed Juncos, Junco hyemalis, Have Better Spatial Memory and Denser Hippocampal Neurons Than Nonmigratory Conspecifics" (Animal Behaviour, Vol. 66, Issue 2, pp. 317-328).One of the
A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population.a. For independent samples of sizes 9 and 4, respectively, find the mean and standard deviation of x1 − x2.b. Must the
A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population.a. For independent samples of sizes 3 and 6, respectively, find the mean and standard deviation of x1 − x2.b. Must
A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6 for the other population.Moreover, the variable is normally distributed on each of the two populations.a. For independent samples of sizes 9 and 4,
A variable of two populations has a mean of 7.9 and a standard deviation of 5.4 for one of the populations and a mean of 7.1 and a standard deviation of 4.6 for the other population.Moreover, the variable is normally distributed on each of the two populations.a. For independent samples of sizes 3
To obtain the sampling distribution of the difference between two sample means for independent samples, as stated in Key Fact 10.1 on page 394, we need to know that, for independent observations, the difference of two normally distributed variables is also a normally distributed variable. In this
In this exercise, you are to perform a computer simulation to illustrate the sampling distribution of the difference between two sample means for independent samples, Key Fact 10.1 on page 394.a. Simulate 1000 samples of size 12 from a normally distributed variable with a mean of 640 and a standard
Regarding the four conditions required for using the pooled t-procedures:a. What are they?b. How important is each condition?
x1 = 468.3, s1 = 38.2, n1 = 6, x2 = 394.6, s2 = 84.7, n2 = 14 We have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case,
Consider the quantities μ1, σ1, x1, s1, μ2, σ2, x2, and s2.a. Which quantities represent parameters and which represent statistics?b. Which quantities are fixed numbers and which are variables?
x1 = 115.1, s1 = 79.4, n1 = 51, x2 = 24.3, s2 = 10.5, n2 = 19 We have provided summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide, in each case,
x1 = 10, s1 = 2.1, n1 = 15, x2 = 12, s2 = 2.3, n2 = 15a. Two-tailed test, α = 0.05b. 95% confidence intervalWe have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t interval procedure to conduct the
x1 = 10, s1 = 4, n1 = 15, x2 = 12, s2 = 5, n2 = 15a. Two-tailed test, α = 0.05b. 95% confidence intervalWe have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t interval procedure to conduct the required
x1 = 20, s1 = 4, n1 = 10, x2 = 18, s2 = 5, n2 = 15a. Right-tailed test, α = 0.05b. 90% confidence intervalWe have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t interval procedure to conduct the required
x1 = 20, s1 = 4, n1 = 10, x2 = 23, s2 = 5, n2 = 15a. Left-tailed test, α = 0.05b. 90% confidence intervalWe have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t interval procedure to conduct the required
x1 = 20, s1 = 4, n1 = 20, x2 = 24, s2 = 5, n2 = 15a. Left-tailed test, α = 0.05b. 90% confidence intervalWe have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t interval procedure to conduct the required
x1 = 20, s1 = 4, n1 = 30, x2 = 18, s2 = 5, n2 = 40a. Right-tailed test, α = 0.05b. 90% confidence intervalWe have provided summary statistics for independent simple random samples from two populations. In each case, use the pooled t-test and the pooled t interval procedure to conduct the required
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,
Discuss the basic strategy for performing a hypothesis test to compare the means of two populations, based on independent samples
In the paper "The Relation of Sex and Sense of Direction to Spatial Orientation in an Unfamiliar Environment" (Journal of Environmental Psychology, Vol. 20, pp. 17-28), J. Sholl et al. published the results of examining the sense of direction of 30 male and 30 female students. After being taken to
V. Tangpricha et al. did a study to determine whether fortifying orange juice with Vitamin D would result in changes in the blood levels of five biochemical variables. One of those variables was the concentration of parathyroid hormone (PTH), measured in picograms/milliliter (pg/mL). The
Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey, Summary of Travel Trends. Independent random samples of 15 midwestern households and 14 southern households provided the following data
In the article "Floral Diversity in Relation to Playa Wetland Area and Watershed Disturbance" (Conservation Biology, Vol. 16, Issue 4, pp. 964-974), L. Smith and D. haukos examined the relationship of species richness and diversity to playa area and watershed disturbance. Independent random samples
In the paper "Outcomes at School Age After Postnatal Dexamethasone Therapy for Lung Disease of Prematurity" (New England Journal of Medicine, Vol. 350, No. 13, pp. 1304-1313), T. Yeh et al. studied the outcomes at school age in children who had participated in a doubleblind, placebo-controlled
Refer to Exercise 10.39 and obtain a 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories.
Refer to Exercise 10.40 and obtain a 98% confidence interval for the difference between the mean absolute pointing errors for males and females.
Refer to Exercise 10.41 and find a 90% confidence interval for the difference between the mean reductions in PTH levels for fortified and unfortified orange juice.
Refer to Exercise 10.42 and determine a 95% confidence interval for the difference between last year's mean VMTs by midwestern and southern households.
Refer to Exercise 10.43 and determine a 95% confidence interval for the difference between the mean number of native species in the two regions.
Why do you need to know the sampling distribution of the difference between two sample means in order to perform a hypothesis test to compare two population means?
Refer to Exercise 10.44 and find a 98% confidence interval for the difference between the mean IQs of school-age children without and with the dexamethasone therapy.
Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper "LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores" (Journal of Nutrition, Vol. 130, pp. 1591-1596), S. Lu et al. compared the daily intake of
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 diabetic mothers. Past studies have shown
An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a regular 2-3/4'' wooden tee to those hit off a 3'' Stinger Competition golf tee. A Callaway Great Big Bertha driver with 10 degrees of loft was used for the test, and a robot swung the
In this section, we introduced the pooled t-test, which provides a method for comparing two population means. In deriving the pooled t-test, we stated that the variablecannot be used as a basis for the required test statistic because Ïƒ is unknown. Why can't that variable be used as a
The formula for the pooled variance, s2p, is given on page 397. Show that, if the sample sizes, n1 and n2, are equal, then s2p is the mean of s21 and s22.
In this exercise, you are to perform a computer simulation to illustrate the distribution of the pooled t-statistic, given in Key Fact 10.2 on page 397.a. Simulate 1000 random samples of size 4 from a normally distributed variable with a mean of 100 and a standard deviation of 16. Then obtain the
As we mentioned on page 403, the following relationship holds between hypothesis tests and confidence intervals: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ1 = μ2 will be rejected in favor of the alternative hypothesis Ha: μ1 = μ2 if and only if the
If the assumptions for a pooled t-interval are satisfied, the formula for a (1 ˆ’ Î±)-level upper confidence bound for the difference, Î¼1 ˆ’ Î¼2, between two population means isFor a left-tailed hypothesis test at the significance level Î±, the null hypothesis H0: Î¼1 = Î¼2 will
If the assumptions for a pooled t-interval are satisfied, the formula for a (1 ˆ’ Î±)-level lower confidence bound for the difference, Î¼1 ˆ’ Î¼2, between two population means isFor a right-tailed hypothesis test at the significance level Î±, the null hypothesis H0: Î¼1 = Î¼2 will
Identify the assumption for using the two-means z-test and the two-means z-interval procedure that renders those procedures generally impractical.
Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions (one for each population) of the variable under consideration are normally distributed and have equal standard deviations. Answer
Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions of the variable under consideration have the same shape, but are not normal, and both sample sizes are large. Answer the following
Suppose that you know that a variable is normally distributed on each of two populations. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. In each case, decide whether you would use the pooled or nonpooled t-test,
Discuss the relative advantages and disadvantages of using pooled and nonpooled t-procedures.
x1 = 10, s1 = 2, n1 = 15, . x2 = 12, s2 = 5, n2 = 15a. Two-tailed test, α = 0.05 b. 95% confidence interval We have provided summary statistics for independent simple random samples from two populations. In each case, use the nonpooled t-test and the nonpooled t-interval procedure to conduct the
x1 = 15, s1 = 2, n1 = 15, . x2 = 12, s2 = 5, n2 = 15a. Two-tailed test, α = 0.05 b. 95% confidence intervalWe have provided summary statistics for independent simple random samples from two populations. In each case, use the nonpooled t-test and the nonpooled t-interval procedure to conduct the

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