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Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions
CHALLENGE More on the complete tree size data set. Use the LONGLEAF data set to repeat the calculations that you performed in Exercises 7.81 and 7.82. Discuss the effect of the sample size on the results.
CHALLENGE Analysis of tree size using the complete data set. The data used in Exercises 7.25(page 442), 7.81, and 7.82 (page 471) were obtained by taking simple random samples from the 584 longleaf pine trees that were measured in the Wade Tract. The entire data set is given in the LONGLEAF data
More on transforming the data. Refer to Exercise 7.119 and the TRAP data for 31 females.Variables that measure concentrations such as this often have distributions that are skewed to the right. For this reason it is common to work with the logarithms of the measured values. Here are the TRAP values
Transforming the data. Refer to Exercise 7.118 and the OC data for 31 females. Variables that measure concentrations such as this often have distributions that are skewed to the right. For this reason it is common to work with the logarithms of the measured values. Here are the OC values
More on the healthy bones study. Refer to the previous exercise. Tartrate resistant acid phosphatase (TRAP) is a biochemical marker for bone resorption that is also measured in blood.Here are the TRAP measurements, in units per liter (U/l), for the same 31 females:19.4 25.5 19.0 9.0 19.1 14.6 25.2
Healthy bones study. Healthy bones are continually being renewed by two processes.Through bone formation, new bone is built;through bone resorption, old bone is removed.If one or both of these processes are disturbed, by disease, aging, or space travel, for example, bone loss can be the result.
CH ALLENGE Alcohol consumption and body composition. Individuals who consume large amounts of alcohol do not use the calories from this source as efficiently as calories from other sources. One study examined the effects of moderate alcohol consumption on body composition and the intake of other
More on sample size and margin of error.Refer to the previous exercise. Make a similar plot and summarize its features for a 99% confidence interval.
Sample size and margin of error. The margin of error for a confidence interval depends on the confidence level, the standard deviation, and the sample size. Fix the confidence level at 95%and the standard deviation at 1 to examine the effect of the sample size. Find the margin of error for sample
Degrees of freedom and t∗. Refer to the previous exercise. Make a similar plot and summarize its features for the value of t∗ for a 90% confidence interval.
Degrees of freedom and confidence interval width. As the degrees of freedom increase, the t distributions get closer and closer to the z (N(0, 1))distribution. One way to see this is to look at how the value of t∗ for a 95% confidence interval changes with the degrees of freedom. Make a plot with
Converting a two-sided P-value. You use statistical software to perform a significance test of the null hypothesis that two means are equal. The software reports P-values for the twosided alternative. Your alternative is that the first mean is greater than the second mean.(a) The software reports t
LSAT scores. The scores of four senior roommates on the Law School Admission Test (LSAT) are 158, 168, 143, 155 Find the mean, the standard deviation, and the standard error of the mean. Is it appropriate to calculate a confidence interval based on these data? Explain why or why not.
Planning a study to compare ad placement.Refer to Exercise 7.80 (page 470), where we compared trustworthy ratings for ads from two different publications. Suppose that you are planning a similar study using two different publications that are not expected to show the differences seen when comparing
CHALLENGE More on planning a study to compare tree size. Refer to the previous exercise.Find the two standard deviations from Exercise 7.81. Do the same for the data in Exercise 7.82, which is a similar setting. These are somewhat smaller than the assumed value that you used in the previous
Planning a study to compare tree size. In Exercise 7.81 (page 471) DBH data for longleaf pine trees in two parts of the Wade Tract are compared. Suppose that you are planning a similar study where you will measure the diameters of longleaf pine trees. Based on Exercise 7.81, you are willing to
Revisiting the storage time study. We studied the loss of vitamin C when bread is stored in Exercise 7.76 (page 470). Recall that two loaves were measured immediately after baking and another two loaves were measured after three days of storage. These are very small sample sizes.(a) Use Table E to
Revisiting the size of trees in the east and west.Tree diameters for the east and west halves of the Wade Tract are compared in Exercise 7.82 (page 471). Using the questions in the previous exercise as a guide, analyze these data.
Revisiting the size of trees in the north and south. The diameters of trees in theWade Tract for random samples selected from the north and south portions of the tract are compared in Exercise 7.81(page 471). Are there statistically significant differences in the standard deviations for these two
More on the dust exposure study. Exercise 7.66(page 468) is similar to Exercise 7.65, but the response variable here is exposure to dust particles that can enter and stay in the lungs. Compare the standard deviations with a significance test and summarize the results. Be sure to comment on the
Revisiting the dust exposure study. The twosample problem in Exercise 7.65 (page 468)compares drill and blast workers with outdoor concrete workers with respect to the total dust that they are exposed to in the workplace. Here it may be useful to know whether or not the standard deviations differ
Revisiting the self-control and food study.Compare the standard deviations of the selfefficacy scores in Exercise 7.64 (page 468). Give the test statistic, the degrees of freedom, and the P-value. Write a short summary of your analysis, including comments on the assumptions for the test.
CHALL ENGE Revisiting the multimedia evaluation study. Mean scores on a knowledge test are compared for two groups of women in Exercise 7.63 (page 468). Compare the standard deviations using an F test. What do you conclude?Comment on the Normal assumption for these data. These standard deviations
An HDL comparison.HDL is also knownas “good”cholesterol. Compare the standard deviations of HDL in Exercise 7.61 (page 467). Give the test statistic, the degrees of freedom, and the P-value.Write a short summary of your analysis, including comments on the assumptions for the test.
Revisiting the cholesterol comparison. Compare the standard deviations of total cholesterol in Exercise 7.61 (page 467). Give the test statistic, the degrees of freedom, and the P-value. Write a short summary of your analysis, including comments on the assumptions for the test.
Comparison of standard deviations. Here are some summary statistics from two independent samples from Normal distributions:Sample n s2 1 10 3.1 2 16 9.3 You want to test the null hypothesis that the two population standard deviations are equal versus the two-sided alternative at the 5% significance
Power and the standard deviation. If the true population standard deviation were 7.0 instead of the 7.4 hypothesized in Example 7.23, would the power for this new experiment be greater or smaller than 0.7965? Explain.
Power and μ1 − μ2. If you repeat the calculation in Example 7.23 for other values of μ1 − μ2 that are larger than 5, would you expect the power to be higher or lower than 0.7965? Why?
The F statistic. The F statistic F = s21/s22is calculated from samples of size n1 = 16 and n2 = 21.(a) What is the upper 5% critical value for this F?(b) In a test of equality of standard deviations against the two-sided alternative, this statistic has the value F = 2.45. Is this value significant
CH ALLENGE Revisiting the effect of storage time on vitamin C. The analysis of the loss of vitamin C when bread is stored in Exercise 7.76 (page 470)is a rather unusual case involving very small sample sizes. There are only two observations per condition(immediately after baking and three days
CHALLENGE Revisiting the dust exposure study. The data on occupational exposure to dust that we analyzed in Exercise 7.65 (page 468) come from two groups of workers that are quite different in size. This complicates the issue regarding pooling because the sample that is larger will dominate the
Again computing the degrees of freedom. Use the Wade Tract data in Exercise 7.82 to calculate the software approximation to the degrees of freedom using the formula on page 460. Verify your calculation with software.
Computing the degrees of freedom. Use the Wade Tract data in Exercise 7.81 to calculate the software approximation to the degrees of freedom using the formula on page 460. Verify your calculation with software.
Revisiting the price of wheat. Example 7.16 (page 456) gives summary statistics for prices received by wheat producers in September and July. The two sample standard deviations are very similar, so we may be willing to assume equal population standard deviations. Calculate the pooled t test
Revisiting the size of trees. Refer to the Wade Tract DBH data in Exercise 7.81 (page 471), where we compared a sample of trees from the northern half of the tract with a sample from the southern half. Because the standard deviations for the two samples are quite close, it is reasonable to analyze
Revisiting self-control and food. You used methods that do not require equal standard deviations when you analyzed the self-efficacy data in Exercise 7.64 (page 468). Can you justify using the pooled procedures for these data? Explain your answer. Analyze the data using these procedures and compare
Revisiting the evaluation of a multimedia program. In Exercise 7.63 (page 468), the knowledge test means for intervention and control groups were compared using the two-sample t procedures that do not assume equal standard deviations. Examine the standard deviations for the two groups and verify
Revisiting the comparison of LDL levels for males and females. In Exercise 7.62 (page 467), the LDL levels for males and females were compared using the two-sample t procedures that do not assume equal standard deviations. Compare the means using a significance test and find the 95%confidence
Breast-feeding versus baby formula. A study of iron deficiency among infants compared samples of infants following different feeding regimens.One group contained breast-fed infants, while the children in another group were fed a standard baby formula without any iron supplements. Here are summary
An improper significance test. A friend has performed a significance test of the null hypothesis that two means are equal. His report states that the null hypothesis is rejected in favor of the alternative that the first mean is larger than the second. In a presentation on his work, he notes that
Sales of a small appliance across months. A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. Suppose that an SRS of 70 stores this month
CHALLENGE Size of trees in the eastern and western halves. The Wade Tract can also be divided into eastern and western halves. Here are the DBHs of 30 randomly selected longleaf pine trees from each half:23.5 43.5 6.6 11.5 17.2 38.7 2.3 31.5 10.5 23.7 East 13.8 5.2 31.5 22.1 6.7 2.6 6.3 51.1 5.4
CH ALLENGE Size of trees in the northern and southern halves. The study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, had several purposes. Are trees in one part of the tract more or less like trees in any other part of the tract or are there differences? In Example 6.1
Does ad placement matter? Corporate advertising tries to enhance the image of the corporation. A study compared two ads from two sources, the Wall Street Journal and the National Enquirer. Subjects were asked to pretend that their company was considering a major investment in Performax, the
Are the samples too small? Refer to Exercises 7.76 and 7.78. Some people claim that significance tests with very small samples never lead to rejection of the null hypothesis. Discuss this claim using the results of these two exercises.
Another ingredient. Refer to Exercise 7.76. The amount of vitamin E (in mg/100 g of flour) in the same loaves was also measured. Here are the data:Immediately after baking: 94.6 96.0 Three days after baking: 97.4 94.3(a) When bread is stored, does it lose vitamin E?To answer this question, perform
Study design matters! Suppose that the researchers in the previous exercise could have measured the same two loaves of bread immediately after baking and again after three days. Assume that the data given had come from this study design. (Assume that the values given in the previous exercise are
Effect of storage time on vitamin C content. Does bread lose its vitamins when stored? Small loaves of bread were prepared with flour that was fortified with a fixed amount of vitamins. After baking, the vitamin C content of two loaves was measured.Another two loaves were baked at the same time,
Why randomize? Refer to the previous exercise. A coworker suggested that you give the flat screens to the next 10 employees who need new screens and the standard monitor to the following 10. Explain why your randomized design is better.
New computer monitors? The purchasing department has suggested that all new computer monitors for your company should be flat screens.You want data to assure you that employees will like the new screens. The next 20 employees needing a new computer are the subjects for an experiment.(a) Label the
Study design is important! Recall Exercise 7.54(page 453). You are concerned that day of the week may affect online sales. So to compare the two Web page designs, you choose two successive weeks in the middle of a month. You flip a coin to assign one Monday to the first design and the other Monday
Effect of the confidence level. Assume x1 = 100, x2 = 120, s1 = 10, s2 = 12, n1 = 50, and n2 = 50.Find a 95% confidence interval for the difference in the corresponding values of μ. Does this interval include more or fewer values than a 99% confidence interval? Explain your answer.
More basic concepts. For each of the following, answer the question and give a short explanation of your reasoning.(a) A significance test for comparing two means gave t = −3.69 with 9 degrees of freedom. Can you reject the null hypothesis that the μ’s are equal versus the two-sided
Basic concepts. For each of the following, answer the question and give a short explanation of your reasoning.(a) A 95% confidence interval for the difference between two means is reported as (−0.1, 1.5). What can you conclude about the results of a significance test of the null hypothesis that
What is wrong? In each of the following situations explain what is wrong and why.(a) A researcher wants to test H0: x1 = x2 versus the two-sided alternative Ha: x1 = x2.(b) A study recorded the IQ scores of 50 college freshmen. The scores of the 24 males in the study were compared with the scores
Beverage consumption. The results in the previous exercise were based on two national surveys with a very large number of individuals. Here is a study that also looked at beverage consumption but the sample sizes are much smaller. One part of this study compared 20 children who were 7 to 10 years
Change in portion size. A recent study of food portion sizes reported that over a 17-year period, the average size of a soft drink consumed by Americans aged 2 years and older increased from 13.1 ounces (oz) to 19.9 oz. The authors state that the difference is statistically significant with P <
Not all dust is the same. Not all dust particles that are in the air around us cause problems for our lungs. Some particles are too large and stick to other areas of our body before they can get to our lungs.Others are so small that we can breathe them in and out and they will not deposit on our
Dust exposure at work. Exposure to dust at work can lead to lung disease later in life. One study measured the workplace exposure of tunnel construction workers.25 Part of the study compared 115 drill and blast workers with 220 outdoor concrete workers. Total dust exposure was measured in milligram
Self-control and food. Self-efficacy is a general concept that measures how well we think we can control different situations. In the study described in the previous exercise, the participants were asked,“How sure are you that you can eat foods low in fat over the next month?” The response was
Evaluating a multimedia program. A multimedia program designed to improve dietary behavior among low-income women was evaluated by comparing women who were randomly assigned to intervention and control groups. The intervention was a 30-minute session in a computer kiosk in the Food Stamp office.24
More on blood lipid levels. Refer to the previous exercise. LDL is also known as “bad”cholesterol. Suppose the researchers wanted to test the hypothesis that LDL levels are higher in sedentary males than in sedentary females. Describe appropriate null and alternative hypotheses and carry out
Comparison of blood lipid levels in males and females. A recent study at Baylor University investigated the lipid levels in a cohort of sedentary university students.23 A total of 108 students volunteered for the study and met the eligibility criteria. The following table summarizes the blood lipid
More on wheat prices. The software outputs in Figure 7.14 give the same value for the pooled and unpooled t statistics. Do some simple algebra to show that this is always true when the two sample sizes n1 and n2 are the same. In other cases, the two t statistics usually differ.
Wheat prices revisited. Figure 7.14 (page 458) gives the outputs from four software packages for comparing prices received by wheat producers in July and September for small samples of 5 producers in each month. Some of the software reports both pooled and unpooled analyses.Which outputs give the
Calculating the degrees of freedom. Assume s1 = 10, s2 = 12, n1 =20, and n2 = 18. Find the software approximate degrees of freedom.
Another two-sample t confidence interval. Assume x1 = 100, x2 =120, s1 = 10, s2 = 12, n1 = 10, and n2 = 10. Find a 95% confidence interval for the difference in the corresponding values of μ using the second approximation for degrees of freedom. Would you reject the null hypothesis that the
Two-sample t confidence interval. Assume x1 = 100, x2 = 120, s1 = 10, s2 = 12, n1 = 50, and n2 = 50. Find a 95% confidence interval for the difference in the corresponding values of μ using the second approximation for degrees of freedom. Does this interval include more or fewer values than a 99%
More on the comparison of twoWeb designs. Consider the previous problem. If the t statistic for comparing the mean hits were 2.75, what P-value would you report? What would you conclude using α = 0.05?
Comparison of two Web designs. You want to compare the daily number of hits for two differentWeb designs that advertise your Internet business. You assign the next 50 days to either Design A or Design B, 25 days to each.(a) Would you use a one-sided or two-sided significance test for this problem?
CHALLENGE Determining the sample size. Consider Example 7.9 (page 434). What is the minimum sample size needed for the power to be greater than 80% when μ = 1.0?
CHALLENGE Sample size calculations. You are designing a study to test the null hypothesis that μ = 0 versus the alternative that μ is positive. Assume that σ is 10. Suppose that it would be important to be able to detect the alternative μ = 2. Perform power calculations for a variety of sample
Power of the comparison of DXA machine operators. Suppose that the bone researchers in Exercise 7.39 wanted to be able to detect an alternative mean difference of 0.002. Find the power for this alternative for a sample size of 15. Use the standard deviation that you found in Exercise 7.39 for these
Insulation study. A manufacturer of electric motors tests insulation at a high temperature (250◦C) and records the number of hours until the insulation fails.16 The data for 5 specimens are 446 326 372 377 310 The small sample size makes judgment from the data difficult, but engineering
Sign test for fuel efficiency comparison. Use the sign test to assess whether the computer calculates a higher mpg than the driver in Exercise 7.35. State the hypotheses, give the P-value using the binomial table (Table C), and report your conclusion.
Sign test for assessment of foreign-language institute. Use the sign test to assess whether the summer institute of Exercise 7.41 improves French listening skills. State the hypotheses, give the P-value using the binomial table (Table C), and report your conclusion.
Another sign test for the comparison of operators. TBBMD values for the same subjects that you studied in the previous exercise are given in Exercise 7.40. Answer the questions given in the previous exercise for TBBMD.
Sign test for the comparison of operators. The differences in the TBBMC measures in Exercise 7.39 can also be analyzed using a sign test. Set up the appropriate null and alternative hypotheses, carry out the test, and summarize the results. How do these results compare with those that you obtained
Sign test for potential insurance fraud. The differences in the repair estimates in Exercise 7.34 can also be analyzed using a sign test. Set up the appropriate null and alternative hypotheses, carry out the test, and summarize the results. How do these results compare with those that you obtained
Property damage due to tornadoes. Table 1.5(page 25) gives the average property damage per year due to tornadoes for each of the 50 states and Puerto Rico. It does not make sense to use the t procedures (or any other statistical procedures)to give a 95% confidence interval for the mean property
IQ test scores. Refer to the IQ test scores for fifth-grade students in Table 1.3 (page 13). Give numerical and graphical summaries of the data and compute a 95% confidence interval. Comment on the validity of the interval.
Length of calls to customer service center.Refer to the lengths of calls to a customer service center in Table 1.1 (page 8). Give graphical and numerical summaries for these data. Compute a 95% confidence interval for the mean call length.Comment on the validity of your interval.
CHALLENGE Assessment of a foreign-language institute. The National Endowment for the Humanities sponsors summer institutes to improve the skills of high school teachers of foreign languages. One such institute hosted 20 French teachers for 4 weeks. At the beginning of the period, the teachers were
Another comparison of DXA machine operators.Refer to the previous exercise. TBBMC measures important variable is total body bone mineral density (TBBMD). This variable is calculated by dividing TBBMC by the area corresponding to bone in the DXA scan. The units are grams per squared centimeter
Comparing operators of a DXA machine. Dualenergy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral content(TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased
A customer satisfaction survey. Many organizations are doing surveys to determine the satisfaction of their customers. Attitudes toward various aspects of campus life were the subject of one such study conducted at Purdue University. Each item was rated on a 1 to 5 scale, with 5 being the highest
More on the level of phosphate in the blood. The normal range of values for blood phosphate levels is 2.6 to 4.8 mg/dl. The sample mean for the patient in the previous exercise falls above this range. Is this good evidence that the patient’s mean level in fact falls above 4.8? State H0 and Ha and
Level of phosphate in the blood. The level of various substances in the blood of kidney dialysis patients is of concern because kidney failure and dialysis can lead to nutritional problems. A researcher performed blood tests on several dialysis patients on 6 consecutive clinic visits. One variable
Fuel efficiency comparison t test. Refer to Exercise 7.24. In addition to the computer calculating mpg, the driver also recorded the mpg by dividing the miles driven by the amount of gallons at fill-up. The driver wants to determine if these calculations are different.Fill-up 1 2 3 4 5 6 7 8 9 10
Potential insurance fraud? Insurance adjusters are concerned about the high estimates they are receiving from Jocko’s Garage. To see if the estimates are unreasonably high, each of 10 damaged cars was taken to Jocko’s and to another garage and the estimates recorded. Here are the results:Car 1
Food intake and NEAT. Nonexercise activity thermogenesis (NEAT) provides a partial explanation for the results you found in the previous analysis. NEAT is energy burned by fidgeting, maintenance of posture, spontaneous muscle contraction, and other activities of daily living. In the study of the
CHALLENGE Food intake and weight gain. If we increase our food intake, we generally gain weight.Nutrition scientists can calculate the amount of weight gain that would be associated with a given increase in calories. In one study, 16 nonobese adults, aged 25 to 36 years, were fed 1000 calories per
Confidence level and interval width. Refer to the previous exercise. Compute the 90% and the 95%confidence intervals. Display the three intervals graphically and write a short explanation of the effect of the confidence level on the width of the interval using your display as an example.
Perceived organizational skills. In a study of children with attention deficit hyperactivity disorder(ADHD), parents were asked to rate their child on a variety of items related to how well their child performs different tasks.11 One item was “Has difficulty organizing work,” rated on a
Do you feel lucky? Children in a psychology study were asked to solve some puzzles and were then given feedback on their performance. Then they were asked to rate how luck played a role in determining their scores.10 This variable was recorded on a 1 to 10 scale with 1 corresponding to very lucky
CH ALLENGE Serum retinol in children. In the Papua New Guinea study that provided the data for the previous two exercises, the researchers also measured serum retinol. A low value of this variable can be an indicator of vitamin A deficiency.Following are the data on the same sample of 40 children
CH ALLENGE More on C-reactive protein in children.Refer to the previous exercise. With strongly skewed distributions such as this, we frequently reduce the skewness by taking a log transformation.We have a bit of a problem here, however, because some of the data are recorded as 0.00 and the
C-reactive protein in children. C-reactive protein(CRP) is a substance that can be measured in the blood. Values increase substantially within 6 hours hours after. In adults, chronically high values have been linked to an increased risk of cardiovascular disease. In a study of apparently healthy
2.3 44.6 31.5 40.3 22.3 43.3 37.5 29.1 27.9(a) Use a histogram or stemplot and a boxplot to examine the distribution of DBHs. Include a Normal quantile plot if you have the necessary software.Write a careful description of the distribution.(b) Is it appropriate to use the methods of this section to
Random distribution of trees t test. A study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, is described in Example 6.1 (page 354). For each tree in the tract, the researchers measured the diameter at breast height (DBH). This is the diameter of the tree at 4.5 feet and the
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