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t birth represents 28.6% of his final height” and that, in prerevolutionary China, the average length of a Chinese boy at birth was 18.9 inches. From this, Seligman deduces that the mean height of mature Chinese men is .9 8 1 66.08 inches, or 5 feet 6.08 inches 8 6 .2 CASE STUDY ❍ 253 He then assumes that the distributi... |
hey had been randomly selected from the two populations. The researcher can, however, randomly select the five samples to be measured with each method. Number the samples from 1 to 10. The five samples selected for the new method may correspond to 5 one-digit random numbers. Use this sequence of random digits generated o... |
Do you believe the death penalty is a deterrrent to crime? • Do you agree that the obstructionist Democrats should not be allowed to gain control of the U.S. Congress in the upcoming elections? Comment on the effect of wording bias on the responses gathered using this survey. STATISTICS AND SAMPLING DISTRIBUTIONS 7.3 W... |
tion is normal, then the sampling distribution of x will also be normal, no matter what sample size you choose. This result can be proven theoretically, but it should not be too difficult for you to accept without proof. • When the sampled population is approximately symmetric, the sampling distribution of x becomes ap... |
if the machine is set to deliver an average fill of 12.1 ounces, the mean fill x of a sample of 10 bottles will be less than 12 ounces with a probability equal to .056. When this danger signal occurs (x is less than 12), the bottler takes a larger sample to recheck the setting of the filling machine. 7.5 EXERCISES EXERCIS... |
RIBUTION OF THE SAMPLE PROPORTION ❍ 275 diameter in the population of patients with AT is no different than the average diameter of the nonaffected tendons (5.97 mm), what is the probability of observing an average diameter of 9.80 or higher? c. What conclusions might you draw from the results of part b? THE SAMPLING D... |
ution? If so, what is its mean and standard deviation? b. What is the probability that the sample proportion ˆp exceeds .25? c. What is the probability that ˆp lies within the interval .25 to .30? d. What might you conclude about p if the sample proportion exceeded .30? 7.44 Prescription Costs The cost of brand-name pr... |
facturer of ballpoint pens randomly samples 400 pens per day and tests each to see whether the ink flow is acceptable. The proportions of pens judged defective each day over a 40-day period are listed in Table 7.7. Construct a control chart for the proportion ˆp defective in samples of n 400 pens selected from the proce... |
ions as S ˆpi p k Create upper and lower control limits as p 3p(1 p) n If a sample proportion exceeds these limits, the process is out of control. 288 ❍ CHAPTER 7 SAMPLING DISTRIBUTIONS The Central Limit Theorem at Work MINITAB provides a perfect tool for exploring the way the Central Limit Theorem works in practice. R... |
dividuals. a. What are the mean and standard deviation of ˆp, the sample proportion with Rh-positive blood type? b. Is the distribution of ˆp approximately normal? Justify your answer. c. What is the probability that the sample proportion ˆp exceeds 82%? d. What is the probability that the sample proportion lies betwee... |
a. The average is between 1100 and 1110. b. The average is greater than 1120. c. The average is less than 900. CASE STUDY CASE STUDY ❍ 295 Sampling the Roulette at Monte Carlo The technique of simulating a process that contains random elements and repeating the process over and over to see how it behaves is called a M... |
ld you test a hypothesis concerning its value? The answer is dictated by the practical question posed and is often determined by personal preference. Since both estimation and tests of hypotheses are used frequently in scientific literature, we include both methods in this and the next chapter. A statistical problem, wh... |
ution The random variable measured is weight, a quantitative random variable best described by its mean m. The point estimate of m, the average weight of all Arctic polar bears, is x 980 pounds. The margin of error is estimated as s 5 10 29.10 29 pounds 1.96 0 n 5 1.96 SE 1.96 †When you sample from a normal distributio... |
e. Display the results of parts b, c, and d graphically, using the form shown in Figure 8.5. Use this display to compare the average room rates for the three hotel chains. 8.19 “900” Numbers Radio and television stations often air controversial issues during broadcast time and ask viewers to indicate their agreement or... |
the 19 that “worked,” or whether it is the one interval that “missed.” Your confidence in the estimated interval follows from the fact that when repeated intervals are calculated, 95% of these intervals will contain m. You can try this experiment on your own using the Java applet called Interpreting Confidence Intervals.... |
r precipitated from a saturated solution of copper sulfate over a 30-minute period. The n 30 students calculated a sample mean and standard deviation equal to .145 and .0051 mole, respectively. Find a 90% confidence interval for the mean amount of copper precipitated from the solution over a 30-minute period. 8.31 Acid ... |
75.8 miles of wear. Based on this confidence interval, can you conclude that there is a difference in the average miles to wearout for the two types of tires? If there were no difference in the two population means, then m1 and m2 would be equal and (m1 m2) 0. If you look at the confidence interval you constructed, you w... |
Find a 95% confidence interval for the difference in the average room rates for the Marriott and the Wyndham hotel chains. b. Find a 99% confidence interval for the difference in the average room rates for the Radisson and the Wyndham hotel chains. d. Do the data indicate a difference in the average room rates between t... |
yers be tested for steroids or other performance enhancing drugs, or not? Suppose that 410 of the baseball fans and 505 of those who are not fans answered yes to this question. a. Construct a 95% confidence interval for the difference in the proportion of adults (fans versus nonfans) who favor mandatory drug testing for... |
nd smallest possible measurements: s Range/4 For this example, suppose that a prior study of the chemical process produced a sample standard deviation of s 21 tons. Then n .24s 2 .24(21)2 105.8 Using a sample of size n 106 or larger, you could be reasonably certain (with probability approximately equal to .95) that you... |
t of beef consumed annually by Americans ranges from 0 to approximately 104 pounds. How many subjects should the researcher select for each group if she wishes to estimate the difference in the average annual per-capita beef consumption correct to within 5 pounds with 99% confidence? 8.76 Red Meat, continued Refer to Ex... |
mist reports the concentration as 4.614, with an “error margin of .006.” a. How would you interpret the chemist’s “error margin”? b. If the reported concentration is based on a random sample of n 30 measurements, with a sample standard deviation s .017, would you agree that the chemist’s “error margin” is .006? 8.95 He... |
at least three years after prison release. 8.111 Specific Gravity If 36 measurements of the specific gravity of aluminum had a mean of 2.705 and a standard deviation of .028, construct a 98% confidence interval for the actual specific gravity of aluminum. 8.112 Audiology Research In a study to establish the absolute thresh... |
ocence and guilt. As the trial begins, the accused person is assumed to be innocent. The prosecution collects and presents all available evidence in an attempt to contradict the innocent hypothesis and hence obtain a conviction. If there is enough evidence against innocence, the court will reject the innocence hypothes... |
ered using the significance level a, the probability of rejecting H0 when H0 is true. Remember that the standard error of x is estimated as s SE n Since the sampling distribution of the sample mean x is approximately normal when n is large, the number of standard deviations that x lies from m0 can be measured using the ... |
7 Standards set by government agencies indicate that Americans should not exceed an average daily sodium intake of 3300 milligrams (mg). To find out whether Americans are exceeding this limit, a sample of 100 Americans is selected, and the mean and standard deviation of daily sodium intake are found to be 3400 mg and 11... |
ition The power of a statistical test, given as 1 b P(reject H0 when Ha is true) measures the ability of the test to perform as required. A graph of (1 b), the probability of rejecting H0 when in fact H0 is false, as a function of the true value of the parameter of interest is called the power curve for the statistical... |
ensity of these plants in both managed and unmanaged sites within the Caucasus region of Russia. In its native area, the average density was found to be 5 plants/m2. In an invaded area in the Czech Republic, 362 ❍ CHAPTER 9 LARGE-SAMPLE TESTS OF HYPOTHESES a sample of n 50 plants produced an average density of 11.17 pl... |
rval you construct contains the value of the parameter specified by H0, then that value is one of the likely or possible values of the parameter and H0 should not be rejected. If the hypothesized value lies outside of the confidence limits, the null hypothesis is rejected at the a level of significance. Construct a 95% co... |
largesample z-test. What is the p-value of this test? b. Construct a 95% confidence interval for (m1 m2). Does this interval confirm your conclusions in part a? 9.28 Noise and Stress In Exercise 8.48, you compared the effect of stress in the form of noise on the ability to perform a simple task. Seventy subjects were di... |
has been effective, state the null hypothesis that should be tested. b. State the alternative hypothesis. c. If 164 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using a .05 and explain the practical conclusions from your test. d. Find the p-v... |
or unlikely observation, assuming that H0 is true and the two population proportions are the same? d. p-value approach: Find the p-value for the test. Test for a significant difference in the population proportions at the 1% significance level. e. Critical value approach: Find the rejection region when a .01. Do the data... |
and Formulas I. Parts of a Statistical Test 1. Null hypothesis: a contradiction of the alterna- tive hypothesis 2. Alternative hypothesis: the hypothesis the researcher wants to support 3. Test statistic and its p-value: sample evidence calculated from the sample data 4. Rejection region—critical values and significanc... |
INT: The maximum value of p(1 p) .25.) 9.67 Losing Weight In a comparison of the mean 1-month weight losses for women aged 20–30 years, these sample data were obtained for each of two diets: Diet I Diet II Sample Size n Sample Mean x Sample Variance s 2 40 10 lb 4.3 40 8 lb 5.7 Do the data provide sufficient evidence t... |
week on the average. Can these workers be viewed as a random sample from among all workers in the industry? a. What are the null and alternative hypotheses to be tested? b. Use the Large-Sample Test of a Population Mean applet to find the observed value of the test statistic. c. Use the Large-Sample Test of a Population... |
olves only the sample mean, x. You can see this phenomenon in Figure 10.1. • The shape of the t distribution depends on the sample size n. As n increases, the variability of t decreases because the estimate s of s is based on more and more information. Eventually, when n is infinitely large, the t and z distributions ar... |
32, does not fall in the rejection region, you cannot reject H0. The data do not present sufficient evidence to indicate that the mean diamond weight exceeds .5 karat. FI GUR E 10. 6 Rejection region for Example 10.3 ● f(t) A 95% confidence interval tells you that, if you were to construct many of these intervals (all o... |
62 .65 .60 .67 Source: Case Study “Pricing of Tuna” Copyright 2001 by Consumers Union of U.S., Inc., Yonkers, NY 10703-1057, a nonprofit organization. Reprinted with permission from the June 2001 issue of Consumer Reports® for educational purposes only. No commercial use or reproduction permitted. www.ConsumerReports.or... |
rees of freedom for the t statistic. Remember that the population variance s 2 describes the shape of the normal distributions from which your samples come, so that either s2 2 would give you an estimate of s 2. But why use just one when information is provided by both? A better procedure is to combine the information ... |
is (x1 x2) D0 ns2 s2 1 n 1 2 2 406 ❍ CHAPTER 10 INFERENCE FROM SMALL SAMPLES When the sample sizes are small, critical values for this statistic are found using degrees of freedom approximated by the formula 2 2 2 s2 s1 n n 2 1 2 2 2/ 2/ n2) n1 df The degrees of freedom are taken to be the integer part of this result. ... |
7 a. Although counts cannot have a normal distribution, do these data have approximately normal distributions? (HINT: Use a histogram or stem and leaf plot.) b. Are you willing to assume that the underlying pop- ulation variances are equal? Why? c. Use the p-value approach to determine whether there is a significant dif... |
) Ha : md 0 d d 0 3. Test statistic: t n n sd/ s d/ where n Number of paired differences d Mean of the sample differences sd Standard deviation of the sample differences 4. Rejection region: Reject H0 when One-Tailed Test Two-Tailed Test t ta (or t ta when the alternative hypothesis is Ha : md 0) t ta/2 or t ta/2 or wh... |
0.41 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). Ten drivers were included in the experiment. Each driver was presented with 40 traffic signs, 20 prohibitive and 20 permissive, in random order. The... |
84398 . . . .0039321 .102587 .351846 .710721 1.145476 1.63539 . . . 7.26094 7.96164 8.67176 9.39046 10.1170 . . . .0157908 .210720 .584375 1.063623 1.610310 2.204130 . . . 8.54675 9.31223 10.0852 10.8649 11.6509 . . . 2.70554 4.60517 6.25139 7.77944 9.23635 10.6446 . . . 22.3072 23.5418 24.7690 25.9894 27.2036 . . . 3.... |
ion instrument is guaranteed to read accurately to within 2 units. A sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 424 ❍ CHAPTER 10 INFERENCE FROM SMALL SAMPLES 355. Test the null hypothesis that s .7 against the alternative s .7. Use a .05. estimate the variance of t... |
ative hypothesis: 1 s 2 2 One-Tailed Test Two-Tailed Test 1 s 2 2 Ha : s 2 (or Ha : s 2 3. Test statistic: 1 s 2 2) Ha : s 2 1 s 2 2 One-Tailed Test Two-Tailed Test s F s where s2 is the larger sample variance 4. Rejection region: Reject H0 when One-Tailed Test Two-Tailed Test F Fa or when p-value a F Fa/2 (continued) ... |
th suppliers, but the manufacturer is concerned about the variability of the impurities from shipment to shipment. If the level of impurities tends to vary excessively for one source of supply, it could affect the quality of the pharmaceutical product. To compare the variation in percentage impurities for the two suppl... |
ade about the populations from which random samples are obtained when the t distribution is used in making small-sample inferences concerning the difference in population means? 10.69 Why use paired observations to estimate the difference between two population means rather than estimation based on independent random s... |
nce in mean leaf area for full-sun versus shade plants? c. Do the data present sufficient evidence to indicate a difference in mean overlap area for full-sun versus shade plants? 10.86 Orange Juice A comparison of the precisions of two machines developed for extracting juice from oranges is to be made using the followi... |
evidence to support the theory that retention of alcohol in the blood is greater at high altitudes? Sea Level 12,000 Feet .07 .10 .09 .12 .09 .13 .13 .17 .15 .14 .10 .14 10.104 Stock Risks The closing prices of two common stocks were recorded for a period of 15 days. The means and variances are x1 40.33 1 1.54 s2 x2 42... |
nt from the national average? Test using a .05. CASE STUDY ❍ 445 b. Use the Small-Sample Test of a Population Mean applet. Do the data provide sufficient evidence to indicate that the average math score for all California students in the class of 2005 is different from the national average? Test using a .05. 10.123 Sur... |
pter 10, the analysis of variance procedures are fairly robust when the sample sizes are equal and when the data are fairly mound-shaped. Violating the assumption of a common variance is more serious, especially when the sample sizes are not nearly equal. 450 ❍ CHAPTER 11 THE ANALYSIS OF VARIANCE ASSUMPTIONS FOR ANALYS... |
ternative hypothesis Ha : At least one of the means is different from the others using the following theoretical argument: • Remember that s 2 is the common variance for all k populations. The quantity SE S MSE k n • is a pooled estimate of s 2, a weighted average of all k sample variances, whether or not H0 is true. I... |
ees of freedom. 11.5 The values of Total SS and SST for the experiment in Exercise 11.4 are Total SS 473.2 and SST 339.8. a. Complete the ANOVA table for Exercise 11.4. b. How many degrees of freedom are associated with the F statistic for testing H0 : m1 m2 m3 m4? c. Give the rejection region for the test in part b fo... |
e June 2001 issue of Consumer Reports® for educational purposes only. No commercial use or reproduction permitted. www.ConsumerReports.org®. a. Use an analysis of variance for a completely ran- domized design to determine if there are significant differences in the prices of tuna packaged in these four different ways. C... |
observations per treatment. The pooled estimator of s 2 is 9.12, and the sample means follow: x1 101.6 x4 92.9 a. Give the value of v that you would use to make pairwise comparisons of the treatment means for a .05. x2 98.4 x5 104.2 x3 112.3 x6 113.8 b. Rank the treatment means using pairwise comparisons. APPLICATIONS ... |
of variance table for this experiment. TABLE 11.3 ● Monthly Phone Costs of Four Companies at Three Usage Levels Company Usage Level A B C D Low Middle High Totals 27 68 308 T1 403 24 76 326 T2 426 31 65 312 T3 408 23 67 300 T4 390 Totals B1 105 B2 276 B3 1246 G 1627 Blocks contain experimental units that are relativel... |
cks. Construct an ANOVA table showing the sources of variation and their respective degrees of freedom. 11.34 The data shown here are observations collected from an experiment that compared EX1134 three treatments, A, B, and C, within each of five blocks, using a randomized block design: Block 11.29 Suppose that the ana... |
art muscles of the four dogs used in the experiment. Are these results of any practical value to the researcher? f. Give the standard error of the difference between the mean calcium uptakes for two levels of digitalis. g. Find a 95% confidence interval for the difference in mean responses between treatments A and B. MI... |
ay that Total SS SSA SSB SS(AB) SSE where • SSA (sum of squares for factor A) measures the variation among the factor A means. • SSB (sum of squares for factor B) measures the variation among the factor B means. • SS(AB) (sum of squares for interaction) measures the variation among the different combinations of factor ... |
A 1 0.0000 0.00000 0.00 1.000 Factor B 1 0.0900 0.09000 1.00 0.338 Interaction 1 3.4225 3.42250 37.85 0.000 Error 12 1.0850 0.09042 Total 15 4.5975 S = 0.3007 R-Sq = 76.40% R-Sq(adj) = 70.50% c. Considering your results in part b, how can you explain the fact that neither of the main effects is significant? d. If a sign... |
, the value of p changes and so does the variance s 2. A similar situation occurs when the response variable is a Poisson random variable—say, the number of industrial accidents per month in a manufacturing plant. Since the variance of a Poisson random variable is s 2 m, the variance changes exactly as the treatment me... |
ity, use the normal probability plot for the residuals. The residuals should exhibit a straight-line pattern, increasing upwards toward the right. 2. To check for equality of variance, use the residuals versus fit plot. The plot should exhibit a random scatter, with the same vertical spread around the horizontal “zero e... |
n age groups 10–19 and 60–69. c. Find a 90% confidence interval for the mean increase in heart rate for the age group 20–39. d. Approximately how many people would you need in each group if you wanted to be able to estimate a group mean correct to within two beats per minute with probability equal to .95? EX1161 11.61 L... |
nder Public Universities Private/Independent Church-Related Males Females $57.3 57.9 56.5 76.5 62.0 47.4 56.7 69.0 63.2 65.3 $85.8 75.2 66.9 73.0 73.0 62.1 69.1 66.5 61.8 76.7 $78.9 69.3 69.7 58.2 61.2 60.4 62.1 59.8 71.9 61.6 Source: Based on “Average Salary for Men and Women Faculty by Category, Affiliation, and Acad... |
similar to, but not the same as, the best-fitting line from the sample. How can you construct a population model to describe the relationship between a random variable y and a related independent variable x? You begin by assuming that the variable of interest, y, is linearly related to an independent variable x. To desc... |
see that SSR is the sum of the squared deviations of the differences between the estimated response without using x ( y) and the estimated response using x (the regression line, yˆ); SSE is the sum of the squared differences between the regression line ( yˆ) and the point y. FI GUR E 1 2. 5 Deviations from the fitted l... |
than an hour. The scores for each of the 15 individuals who took both tests are given in the next table. Applicant Test 1 (x) Test 2(y 10 11 12 13 14 15 75 89 60 71 92 105 55 87 73 77 84 91 75 82 76 38 56 35 45 59 70 31 52 48 41 51 58 45 49 47 a. Construct a scatterplot for the data. Does the assumption of linearity a... |
ction 12.4. The sum of squares for regression, SSR, in the analysis of variance measures the portion of the total variation, Total SS Syy, that can be explained by the regression of y on x. The remaining portion, SSE, is the “unexplained” variation attributed to random error. One way to measure the strength of the rela... |
be linear if x varied over a wider range (say, x 4 to x 48)? c. How do you describe the strength of the relation- ship between y and x? d. What is the best estimate of the common population variance s 2? e. Find a 95% confidence interval for the slope of the line. 12.24 Strawberries II The following data (Exercise 12.16... |
ted Value 450 500 550 Normal Probability Plot of the Residuals (response is y) 50 25 0 Residual 25 50 526 ❍ CHAPTER 12 LINEAR REGRESSION AND CORRELATION 12.34 Laptops and Learning, again Refer to the data given in Exercise 12.25. The MINITAB printout is reproduced here. Regression Analysis: y versus x The regression eq... |
ence bands are narrower than the prediction bands for every value of the achievement test score x. Certainly you would expect predictions for an individual value to be much more variable than estimates of the average value. Also notice that the bands seem to get wider as the value of x0 gets farther from the mean x. Th... |
(60. ) 4 or r .83. This value of r is fairly close to 1, the largest possible value of r, which indicates a fairly strong positive linear relationship between height and weight. There is a direct relationship between the calculational formulas for the correlation coefficient r and the slope of the regression line b. S... |
resulted in a large number of “low-fat” or “fat-free” products. The table shows the number of calories and the amount of sodium (in milligrams) per slice for five different brands of fat-free American cheese. Brand Sodium (mg) Calories Kraft Fat Free Singles Ralphs Fat Free Singles Borden® Fat Free Healthy Choice® Fat F... |
hosphorus levels y to the amount of phosphorus applied to the soil x. Graph the least-squares line as a check on your answer. c. Do the data provide sufficient evidence to indicate that the amount of phosphorus present in the plant is linearly related to the amount of phosphorus applied to the soil? d. Estimate the mea... |
data. b. Construct the ANOVA table. c. Is there sufficient evidence to indicate that the yield of oats is linearly related to the amount of nitrogen applied? Use a .05. d. Predict the expected yield of oats with 95% confi- dence if 250 pounds of nitrogen per acre are applied. SUPPLEMENTARY EXERCISES ❍ 547 e. Estimate th... |
L OBJECTIVES In this chapter, we extend the concepts of linear regression and correlation to a situation where the average value of a random variable y is related to several independent variables—x1, x2, . . . , xk—in models that are more flexible than the straight-line model of Chapter 12. With multiple regression anal... |
of the MINITAB printout in Figure 13.3. There are n 15 observations and k 4 independent predictor variables. You can verify that the total degrees of freedom, (n 1) 14, is divided into k 4 for regression and (n k 1) 10 for error. FI GUR E 13. 3 A portion of the MINITAB printout for Example 13.2 ● S = 6.84930 R-Sq = 97... |
e of the others. If you choose to compare several different models, use R2(adj) to compare their effectiveness. 5. Use computer-generated residual plots to check for violation of the regression assumptions. A quadratic equation is y a bx cx2. The graph forms a parabola. Once all of these steps have been taken, you are ... |
egression 2 234.96 117.48 332.53 0.000 Residual Error 3 1.06 0.35 Total 5 236.02 Source DF Seq SS x 1 227.82 x-sq 1 7.14 a. Plot the data points. Does it look as though the quadratic model is necessary? b. Find s on the printout. Confirm that kE s n 1 SS c. Do the data provide sufficient evidence to indicate that the mo... |
redictor variables, qualitative predictor variables are entered into a regression model through dummy or indicator variables. For example, in a model that relates the mean salary of a group of employees to a number of predictor variables, you may want to include the employee’s ethnic background. If each employee includ... |
exactly the same as the equation in part b except that we have added the term x1x2. How does the addition of the x1x2 term affect the graphs of the three lines? d. What flexibility is added to the first-order model E(y) b0 b1x1 b2x2 by the addition of the term b3x1x2, using the model E(y) b0 b1x1 b2x2 b3x1x2? 13.19 A mu... |
t tests, you might want to test hypotheses about some subsets of these regression coefficients. For example, suppose a company suspects that the demand y for some product could be related to as many as five independent variables, x1, x2, x3, x4, and x5. The cost of obtaining measurements on the variables x3, x4, and x5 ... |
ion analysis is an easy way to locate some variables that contribute information for predicting y, but it is not foolproof. Since these programs always fit first-order models of the form E(y) b0 b1x1 b2x2 bkxk they are not helpful in detecting curvature or interaction in the data. The stepwise regression analysis is best... |
must be entered into the first (k 1) columns of the MINITAB worksheet. Once this is done, the main inferential tools for linear regression analysis are generated using Stat Regression Regression. The Dialog box for the Regression command is shown in Figure 13.21. Select y for the Response variable and x1, x2, . . . , x... |
1-sq 0.11350 0.02945 3.85 0.001 x2 -21.699 9.224 -2.35 0.030 x1x2 0.8730 0.3589 2.43 0.026 x1sqx2 -0.008869 0.003257 -2.72 0.014 S = 2.90763 R-Sq = 89.8% R-Sq(adj) = 87.0% Analysis of Variance Source DF SS MS F P Regression 5 1346.45 269.29 31.85 0.000 Residual Error 18 152.18 8.45 Total 23 1498.63 Source DF Seq SS x1 ... |
an only happen when b1 b2 b3 0. Use the MINITAB printout for the one-way ANOVA shown below to perform the test for equality of treatment means. Verify that this test is identical to the test for significant regression in Exercise 13.32. MINITAB output for Exercise 13.33 One-Way ANOVA: Light Water, White Oil, White Water... |
of a study to explore the attitudes of young adults toward the services provided by libraries. 594 14.1 A DESCRIPTION OF THE EXPERIMENT ❍ 595 A DESCRIPTION OF THE EXPERIMENT 14.1 Many experiments result in measurements that are qualitative or categorical rather than quantitative; that is, a quality or characteristic (... |
Avoid declaring a causal relationship between color and preference! EXAMPLE 14.2 TABLE 14.2 Degrees of freedom for a simple goodness-of-fit test: df k 1 14.3 TESTING SPECIFIED CELL PROBABILITIES: THE GOODNESS-OF-FIT TEST ❍ 599 The proportions of blood phenotypes A, B, AB, and O in the population of all Caucasians in the... |
an array called a contingency table. A total of n 309 furniture defects were recorded and the defects were classified into four types: A, B, C, or D. At the same time, each piece of furniture was identified by the production shift in which it was manufactured. These counts are presented in a contingency table in Table 14... |
00 and the results are declared highly significant. That is, the null hypothesis is rejected. There is sufficient evidence to indicate a relationship between treatment and incidence of flu. FI GUR E 1 4. 3 MINITAB output for Example 14.5 ● Chi-Square Test: No Vaccine, One Shot, Two Shots Expected counts are printed below... |
in advance. In another flu prevention experiment like Example 14.5, the experimenter decides to search the clinic records for 300 patients in each of the three treatment categories: no vaccine, one shot, and two shots. The n 900 patients will then be surveyed regarding their winter flu history. The experiment results in ... |
247 1120 99 5.9 17.9 16.4 21.4 21.1 14.2 11.0 EX1433 14.33 How Big Is the Household? A local chamber of commerce surveyed 120 households in their city—40 in each of three types of residence (apartment, duplex, or single residence)—and Type of Residence Family Members 1 2 3 4 or more Apartment Duplex Single Residence 8... |
in:” blank. Make sure that the square labeled “Display Counts” is checked. Click the Chi-Square . . . button to display the dialog box in Figure 14.6. Check the boxes for “Chi-Square Analysis” and “Expected Cell Counts.” Click OK twice. This sequence of commands not only tabulates the contingency table, but also perfor... |
US.”15 Use the table that follows to determine if there is a significant difference in the contamination rate at three processing plants. One hundred turkeys were randomly selected from each of the processing lines at these three plants. Salmonella Present Plant Sample Size 1 2 3 42 23 22 100 100 100 Is there a significa... |
n a cherry-flavored suspension used to treat bacterial infections in children. To compare the taste of their product with three competing medications, Pfizer tested 50 healthy children and 20 healthy adults. Among other taste-testing measures, they recorded the number of tasters who rated each of the four antibiotic susp... |
in the last column labeled P(x 2) is the p-value for testing the hypothesis of no difference in the proportion of students and nonstudents who answer each question favorably. Hence, each question gives rise to a 2 2 contingency table. 1. Perform a test of homogeneity for each question and verify the reported p-value of... |
rejection of H0. The null hypothesis of equality of the two distributions should be rejected if the observed value of the test statistic T is less than or equal to 56. TABLE 15.2 ● Table 7 in Appendix I A Portion of the 5% Left-Tailed Critical Values, n2 10 4 9 10 4 10 11 12 13 14 15 16 17 n1 5 19 20 21 23 24 26 6 7 8... |
m test to determine whether population 1 is shifted to the left of population 2. 1 as the test statistic? Sample 1 Sample . State the null and alternative hypotheses to be tested. b. Rank the combined sample from smallest to largest. Calculate T1 and T * 1. c. What is the rejection region for a .05? d. Do the data prov... |
umber of “plus” signs in the table—is x 1, and the p-value is calculated as p-value 2P(x 1) 2(.011) .022 The fairly small p-value .022 allows you to reject H0 at the 5% level. There is significant evidence to indicate that the number of defective fuses is not the same for the two production lines; in fact, line B produc... |
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