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statistics alive

Questions and Answers of Statistics Alive

Find the tabled value of t ( ta ) corresponding to a right-tail area a and degrees of freedom given 6. a=.10, df = 7
Find the tabled value of t ( ta ) corresponding to a left-tail area a and degrees of freedom given 7. a=.01, df = 9
Find the tabled value of t ( ta ) corresponding to a left-tail area a and degrees of freedom given 8. a = .05, df = 8
Find the tabled value of t ( ta ) corresponding to a left-tail area a and degrees of freedom given 9. a=.025, df =15
Find the critical value(s) of t that specify the rejection region for the situations given 5. A left-tailed test with a = .01 and 7 df
Find the critical value(s) of t that specify the rejection region for the situations given 6. An upper one-tailed test with a = .05 and 11 df
19. The following n510 observations are a sample from a normal population:a. Find the mean and standard deviation of these data.b. Find a 99% upper one-sided confidence bound for the population mean
20. Cerebral Blood Flow Cerebral blood flow (CBF) in the brains of healthy people is normally distributed with a mean of 74. A random sample of 25 stroke patients resulted in an average CBF of x
21. Red Pine The main stem growth measured for a sample of seventeen 4-year-old red pine trees produced a mean and standard deviation equal to 28.7 and 8.6 centimeters, respectively. Find a 90%
22. Cheese, Please Here are the prices per serving of n513 different brands of individually wrapped cheese slices:Construct a 95% confidence interval estimate of the underlying average price per
23. Tuna Fish Is there a difference in the prices of tuna, depending on the method of packaging?Consumer Reports gives the estimated average price for a variety of different brands of tuna, based on
24. Dissolved O2 Content A state agency requires a minimum of 5 parts per million (ppm) of dissolved oxygen in order for the oxygen content to be sufficient to support aquatic life. Six water
25. Lobsters In a study of the infestation of a particular species of lobster by two types of barnacles, the body lengths (in millimeters) of 10 randomly selected lobsters are measured:Find a 95%
26. Smoking and Lung Capacity In a study of the effect of cigarette smoking on the carbon monoxide diffusing capacity (DL) of the lung, researchers found that current smokers had DL readings
27. Ben Roethlisberger The number of passes completed by Ben Roethlisberger, quarterback for the Pittsburgh Steelers, was recorded for each of the 15 regular season games in which he played during
28. Purifying Organic Compound A chemist prepared ten 4.85 g quantities of aniline and purified it to acetanilide using fractional crystallization. The following dry yields were recorded:Estimate the
18. Test Scores The test scores on a 100-point test were recorded for 20 students:a. Can you reasonably assume that these test scores have been selected from a normal population? Use a stem and leaf
17. A random sample of n512 observations from a normal population produced x 547.1 and s2 54.7. Test the hypothesis H : m 548 0 against H :m±48 a at the 5% level of significance.
Find the critical value(s) of t that specify the rejection region for the situations given 7. A two-tailed test with a = .05 and 7 df
Find the critical value(s) of t that specify the rejection region for the situations given 8. A lower one-tailed test with a =.01 and 15 df
Use Table 4 in Appendix I to approximate the p-value for the t statistic in the situations given 9. A two-tailed test with t = 2.43 and 12 df
Use Table 4 in Appendix I to approximate the p-value for the t statistic in the situations given 10. A right-tailed test with t = 3.21 and 16 df
Use Table 4 in Appendix I to approximate the p-value for the t statistic in the situations given 11. A two-tailed test with t = -1.19 and 25 df
Use Table 4 in Appendix I to approximate the p-value for the t statistic in the situations given 12. A left-tailed test with t = -8.77 and 7 df
Use Table 4 in Appendix I to bound the p-values given 13. P(t>1.2) with 5 df
Use Table 4 in Appendix I to bound the p-values given 14. P(t>2)+P(t
Use Table 4 in Appendix I to bound the p-values given 15. P(t
Use Table 4 in Appendix I to bound the p-values given 16. P(t>0.6) with 12 df
29. Organic Compounds, continued Refer to Exercise 28. Approximately how many 4.85 g specimens of aniline are required if you wish to estimate the mean number of grams of acetanilide correct to
Use the data given to test the given alternative hypothesis.Find the p-value for the test. Construct a 95% confidence interval for σ12 / σ22 13. Sample Size Sample Variance 13 13 18.3 7.9 H > a
(Paired t-Test) Refer to the tire wear data from Table 10.3.1. To perform a paired-difference test for these dependent samples, enter the data into the first two columns of an Excel spreadsheet and
(One-Sample t-Test) Refer to Example 10.3, in which the average weight of diamonds using a new process was compared to an average weight of .5 karat.1. Enter the six recorded weights—.46, .61, .52,
(Two-Sample t-Test Assuming Equal Variances) The test scores on the same algebra test were recorded for eight students randomly selected from students taught by teacher A and nine students randomly
(Two-Sample t-Test Assuming Unequal Variances)1. Refer to Example 10.21. If the ratio of the two sample variances had been so large that you could not assume equal variances (we use “greater than
(One-Sample t-Test) Refer to Example 10.3, in which the average weight of diamonds using a new process was compared to an average weight of .5 karat.1. Select stat ➤ EDIT and enter the six recoded
(Two-Sample t-Test Assuming Equal Variances) The test scores on the same algebra test were recorded for eight students randomly selected from students taught by Teacher A and nine students randomly
(Two-Sample t-Test Assuming Unequal Variances)1. Refer to Example 10.25. If the ratio of the two sample variances had been so large that you could not assume equal variances (we use “greater than
1. Impurities A manufacturer can tolerate a small amount (.05 milligrams per liter (mg/L)) of impurities in a raw material needed for manufacturing its product.To test for impurities in a particular
2. Sodium Hydroxide The object of a general chemistry experiment is to determine the amount (in milliliters) of sodium hydroxide (NaOH) solution needed to neutralize 1 gram of a specified acid. This
3. Sea Urchins An experimenter was interested in determining the mean thickness of the cortex of the sea urchin egg. The thickness was measured for n510 sea urchin eggs. The following measurements
(Two-Sample t-Test Assuming Unequal Variances)1. Refer to Example 10.17. If the ratio of the two sample variances had been so large that you could not assume equal variances (we use “greater than
(Two-Sample t-Test Assuming Equal Variances) The test scores on the same algebra test were recorded for eight students randomly selected from students taught by teacher A and nine students randomly
14. Fabricating Systems A production plant has two fabricating systems, both of which are maintained at 2-week intervals. However, one system is twice as old as the other. The number of finished
15. Orange Juice A comparison of the precisions of two machines developed for extracting juice from oranges is to be made using the following data:a. Is there sufficient evidence to indicate that
16. SAT Scores The SAT subject tests in chemistry and physics for two groups of 15 students each electing to take these tests are given here.To use the two-sample t-test with a pooled estimate of 2
17. Lithium Batteries The stability of measurements on a manufactured product is important in maintaining product quality. A manufacturer of lithium batteries suspected that one of the production
18. Brees and Wilson Quarterbacks not only need to have a good passing percentage, but they need to be consistent. That is, the variability in the number of passes completed per game should be small.
19. Tuna III In Exercise 15 (Section 10.3), you conducted a test to detect a difference in the average prices of light tuna in water versus light tuna in oil.Summarized data on the average price of
20. Runners and Cyclists III An experiment was conducted involving 10 healthy runners and 10 healthy cyclists to determine if there are significant differences in pressure measurements within the
21. Impurities A pharmaceutical manufacturer is concerned about the variability of the impurities from shipment to shipment from two different suppliers.To compare the variation in percentage
22. Stock Risks The closing prices of two common stocks were recorded for a period of 15 days. The means and variances area. Do these data present sufficient evidence to indicate a difference between
23. Bees Insects hovering in flight expend enormous amounts of energy for their size and weight. The data shown here were taken from a much larger body of data collected by T.M. Casey and
4. Fossils The data in the table are the diameters and heights of 10 fossil specimens of a species of small shellfish that were unearthed in a mapping expedition near the Antarctic Peninsula.16 The
5. Fossils, continued Refer to Exercise 4. Suppose you want to estimate the mean diameter of the fossil specimens correct to within 5 millimeters with probability equal to .95. How many fossils do
18. Connector Rods A producer of machine parts claimed that the diameters of the connector rods produced by his plant had a variance of at most 18.75 millimeters2.A random sample of 15 connector rods
19. Arranging Objects The following data are the response times in seconds for n=25 first graders to arrange three objects by size.Find a 95% confidence interval for the average response time for
20. The NBA Finals Want to attend a pro-basketball game? The average resale prices for the NBA rematch of the Cleveland Cavaliers and the Golden State Warriors in 2017 compared to the average ticket
21. Mall Rats An article in American Demographics investigated consumer habits at the mall. We tend to spend the most money shopping on the weekends, and, in particular, on Sundays from 4 to 6 p.m.
22. Got Milk? A dairy in the market for a new container-filling machine is considering two models, manufactured by companies A and B. Other factors being the same for the two models, the deciding
23. Got Milk II Refer to Exercise 22. Wishing to demonstrate that the variability of fills is less for her model than for her competitor’s, a sales representative for company A acquired a sample of
24. Runners and Cyclists II In the study reported earlier involving runners and cyclists, the level of creatine phosphokinase (CPK) in blood samples, a measure of muscle damage, was determined for
25. Auto Design An experiment is conducted to compare two new automobile designs. Twenty people are randomly selected, and each person is asked to rate each design on a scale of 1 (poor) to 10
1. Suppose that you wish to test for significant improvement in scores from 2016 to 2017 for each of the groups Grade 4–8 and Grade 9–12. Conduct the appropriate tests using a =.05.The school
2. Find 95% lower bounds for the mean increases in scores from 2016 to 2017.The school accountability movement has relied in large part on standardized test scores to evaluate students, schools,
17. Alcohol and Altitude The effect of alcohol consumption on the body appears to be much greater at high altitudes than at sea level. To test this theory, one group of 6 randomly selected
16. Reaction Times III A psychologist wishes to verify that a certain drug increases the reaction time to a given stimulus. The following reaction times (in tenths of a second) were recorded before
6. Ring-Necked Pheasants The weights in grams of 10 males and 10 female juvenile ring-necked pheasants are given here.a. Use a statistical test to determine if the population variance of the weights
7. Calcium The calcium (Ca) content of a powdered mineral substance was analyzed 10 times with the following percent compositions recorded:a. Find a 99% confidence interval for the true calcium
8. Sun or Shade? Researchers examined the differences in a particular plant when grown in full sunlight versus shade conditions.17 In this study, shaded plants received direct sunlight for less than
9. Price Wars Many seniors are ordering their drugs online to take advantage of lower costs for these pharmacies. A random sample of nine online pharmacies was selected and the cost of a 10-mg
10. Breathing Patterns Research psychologists measured the baseline breathing patterns—the total ventilation (in liters of air per minute)adjusted for body size—for each of n530 patients, so that
11. Reaction Times A comparison of reaction times (in seconds) for two different stimuli in an experiment produced the following results when applied to a random sample of 16 people:Do the data
12. Reaction Times II Refer to Exercise 11.Suppose that the experiment is conducted using eight people as blocks and making a comparison of reaction times within each person; that is, each person is
13. Refer to Exercises 11 and 12. Calculate a 95% confidence interval for the difference in the two population means for each of these experimental designs. Does it appear that blocking increased the
14. Chemical Purity A chemical manufacturer claims that the purity of his product never varies by more than 2%. Five batches were tested and given purity readings of 98.2, 97.1, 98.9, 97.7, and
15. 16-Ounce Cans? A cannery prints “weight 16 ounces” on its label. The quality control supervisor selects nine cans at random and weighs them. She finds x515.7 and s5.5. Do the data present
3. Summarize your results on the progress of students from 2016 to 2017 in the form of a report.The school accountability movement has relied in large part on standardized test scores to evaluate
Use the data given to test the given alternative hypothesis.Find the p-value for the test. Construct a 95% confidence interval for σ12 / σ22 12. Sample Size Sample Variance 180 20 55.7 31.4 H 00 2
13. Auto Insurance The cost of auto insurance in California is dependent on many variables, such as the city you live in, the number of cars you insure, and your insurance company. The website
A cement manufacturer claims that concrete prepared from his product has a relatively stable compressive strength and that the strength measured in kilograms per square centimeter(kg/cm2 ) lies
An experimenter is convinced that her measuring instrument had a variability measured by standard deviation  52. During an experiment, she recorded the measurements 4.1, 5.2, and 10.2. Do these
Find the tabled value for a x2 variable based on n-1 degrees of freedom with an area of a to its right. 1. n 10, a .05
Find the tabled value for a x2 variable based on n-1 degrees of freedom with an area of a to its right. 2. n 25, a .95
Find the tabled value for a x2 variable based on n-1 degrees of freedom with an area of a to its right. 3. n 41, a .025
Find the tabled value for a x2 variable based on n-1 degrees of freedom with an area of a to its right. 4. n 8, a .99
Find the tabled value for a x2 variable based on n-1 degrees of freedom with an area of a to its right. 5. n 18, a .90
Find the tabled value for a x2 variable based on n-1 degrees of freedom with an area of a to its right. 6. n 30, a .005
Use the information to test Ho: σ2 = σo2 versus the given alternate hypothesis. Construct a (1-a)100% confidence interval for σ2 using the x2 statistic. 7. n=25, x=126.3, s = 21.4, H: 2>15,
Use the information to test Ho: σ2 = σo2 versus the given alternate hypothesis. Construct a (1-a)100% confidence interval for σ2 using the x2 statistic. 8. n=15, x=3.91, s=.3214, H: o.5, a =
Check your ability to use Table 5 in Appendix I by verifying the following statements:1. The probability that 2 x , based on n516 measurements (df 515), exceeds 24.9958 is .05.2. For a sample of n56
24. Two Different Entrees To compare the demand for two different entrees, A and B, a cafeteria manager recorded the number of purchases of each entree on seven consecutive days. Do the data provide
14. America’s Market Basket A survey was conducted by an independent price-checking company to check an advertiser’s claim that it had lower prices than its competitors. The average weekly total,
15. No Left Turn An experiment was conducted to compare the mean reaction times to two types of traffic signs: prohibitive (No Left Turn) and permissive(Left Turn Only). Each of 10 drivers was
16. Healthy Teeth II In an experiment to study an oral rinse designed to prevent plaque buildup, subjects were divided into two groups: One group used a rinse with an antiplaque ingredient, and the
17. Ground or Air? The earth’s temperature can be measured using ground-based sensoring which is accurate but tedious, or infrared-sensoring which appears to introduce a bias into the temperature
18. Red Dye To test the comparative brightness of two red dyes, nine samples of cloth were divided into two pieces. One of the two pieces in each sample was randomly chosen and red dye 1 applied; red
19. Tax Assessors In response to a complaint that a particular tax assessor (1) was biased, an experiment was conducted to compare the assessor named in the complaint with another tax assessor(2)
20. Memory Experiments Twenty students participated in an experiment in which they were first asked to recall a list of 25 words. They were then given a second list, and asked to form images of the
21. Music in the Workplace Before contracting to have music piped into each of his suites of offices, an executive randomly selected seven offices and had the system installed. The average time(in
23. Safety Programs Data were collected on lost-time accidents (mean work-hours lost per month over a period of 1 year) before and after an industrial safety program was put into effect at six

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