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probability statistics
Statistics And Probability With Applications For Engineers And Scientists Using MINITAB R And JMP 2nd Edition Irwin Guttman, Kalanka P. Jayalath, Bhisham C. Gupta - Solutions
A nutritionist investigates the impact of type of breakfast on midmorning concentration. He puts together a sample of 50 adults. He feeds them a breakfast and 4 hours later measures their concentration on an interval-level concentration test. On one day he feeds them bacon and eggs, on a second day
Some parents demand that their children friend them on Facebook and other parents don’t. A developmental psychologist wondered if such parental supervision had any impact on behavior. She obtained a sample of first-year college students and classified them as having parents who were or were not
An adhesives researcher tests the holding power of a wood glue under different humidities. He glues together 100 small pieces of wood and randomly assigns each one to sit for an hour in a room with either 10%, 30%, 50%, 70%, or 90% relative humidity. Each glued piece of wood is then tested to see
The higher the percentage of variability in the dependent variable explained by the explanatory variable, the_____is the size of the effect. (p. 18)
One determines if an F ratio is statistically significant by comparing F to_____. (p. 18)
Interpretation of results for a statistically significant ANOVA differs from t in that it has to address where the_____is located. (p. 18)
SSTotal — SSBetween = _____? (p. 18)
SSBetween, isolates the variability in scores that is primarily due to_____. (p. 18)
SSTotal can be broken down into two components: _____and_____. (p. 18)
To calculate_____, the grand mean is subtracted from each score, the difference scores are squared, and they are all added up. (p. 18)
Numerators in variance formulas are_____. (p. 18)
ΣX 2is called a_____.
If F = Fcv, the null hypothesis is_____. (p. 18)
In order to calculate total degrees of freedom for a betweensubjects, one-way ANOVA, one could add together_____and_____. (p. 18)
The denominator degrees of freedom for a between-subjects, oneway ANOVA F ratio is df_____. (p. 18)
The numerator degrees of freedom for a between-subjects, one-way ANOVA F ratio is df_____. (p. 18)
The critical value of F depends on the degrees of freedom for the_____and the degrees of freedom for the_____of the F value. (p. 18)
The decision rule for a between-subjects, one-way ANOVA says that if F falls in the rare zone of the sampling distribution, the null hypothesis is_____. (p. 18)
The alternative hypothesis says that at least _____population mean is different from at least_____other population mean. (p. 18)
The null hypothesis for a between-subjects, one-way ANOVA is always_____directional. (p. 18)
The null hypothesis states that there is _____mean difference between any of the populations. (p. 18)
The assumption that the variability in all groups is about the same is called the_____ assumption. (p. 18)
Between-subjects, one-way ANOVA assumes that the dependent variable in each population is_____distributed. (p. 18)
For a between-subjects, one-way ANOVA, the cases in each group should be_____from the population. (p. 18)
The assumptions for between-subjects, oneway ANOVA are the same as they are for_____. (p. 18)
The categories of an explanatory variable in ANOVA are called_____.
Four groups are being compared in a between-subjects, one-way ANOVA. Each group has 10 cases. MSWithin = 77.89 and dfWithin =36. The F ratio was statistically significant with α = .05.a. Use this information to complete a post-hoc test comparing M1 = 29.00 and M2 = 18.00; interpret the difference
Given SSBetween = 1,827.50 and SSTotal = 4,631.50, (a) calculate r 2and (b) comment on the size of the effect.
Given α = .05, Fcv = 2.690, dfBetween = 4, dfWithin. = 30, and F = 7.37, write the results in APA format.
Given dfBetween = 3,dfWithin =12,dfTotal =15, SSBetween= 716.00, SSWithin = 228.00, and SSTotal = 944.00, complete an ANOVA summary table. (p. 18) Group 1 Group 2 Group 3 X x X x X x 16 256 19 361 26 676 18 324 20 400 22 484 14 196 22 484 25 625 Grand 18 324 24 576 27 729 X x 66.00 1,100.00 85.00
Given the data in the table below, calculate (a) SSTotal,(b)SSBetween, and (c) SSWithin. (p. 18)
Here are data on an interval-level variable for three independent samples. Prepare this table so that it would be ready for use in computing sums of squares. (Do not compute the sums of squares.) (p. 18)
If a between-subjects, one-way ANOVA has 32 cases randomly assigned to four equally sized group, what are dfBetween,dfWithin,and dfTotal? (p. 18)
If the numerator df for a between-subjects, one-way ANOVA are 4 and the denominator df are 20, what is the decision rule if α = .05? (p. 18)
Select the correct test for this example: A human factors psychologist is comparing three different adhesives used in sealing cereal boxes to see which one is easiest to open. He obtained 90 consumers, randomly assigned each participant to open one cereal box, and measured how long it took to open
Select the correct test for this example: A gerontologist wants to determine which exercise program, yoga or stretching, leads to greater limberness in elderly people. He uses a ratio-level range-ofmotion test to measure limberness and randomly assigns elderly people to receive either eight weeks
When is a post-hoc test used? (p. 18)
An F ratio is a ratio of what divided by what? (p. 18)
What makes up between-group variability? (p. 18)
What makes up within-group variability? (p. 18)
If N = 77, M1 = 48, M2 = 44, and SM1−M2, report the results in APA format.
An education researcher randomly assigns 36 15-year-olds either to study a driver’s manual online or to review a print-out of the same document. She then has each teenager take a multiple-choice test. What statistical test should she use to see if modality of studying, online vs.paper, has an
A researcher knows that stimulants are used to treat ADHD. He is curious if caffeine, a stimulant, has an impact on ADHD symptoms. He takes a sample of children who have been diagnosed with ADHD but who are not on medication. One by one, he places each child in a chair to watch a very boring,
Michael completed a study. In the interpretation, he expressed a concern that there was an effect, but that his study had failed to find it.Michael had:___rejected the null hypothesis.___failed to reject the null hypothesis.___done an independent-samples t test.___done a paired-samples t
Based on Meghan’s results in Question 9, Taylor has decided to replicate the study at her college, but as a one-tailed independentsamples t test, α = .05. Her alternative hypothesis is that μMen> μwomen, and for the numerator of her t test, she uses MMen — MWoman. Don’t worry about the
Meghan used an independent-samples t test to compare the salaries of male professors to those of female professors at her college. To help interpret her results, she calculated a 95%CI for the difference between population means and found that it ranged from $2,563 to $42,985. The difference was in
Adele is planning to complete a single-sample t test comparing the GPA of the small number of male psych majors graduating this semester (n =10) to the GPA of the larger number of female psych majors who are graduating (n = 17). What df should she use?
Derek completes a single-sample z test with 55 cases, where μ = 10.6, M= 12.9, and z = 1.70. Report the results in APA format.
Given N = 36, M = 55, μ= 57, and σ = 12, calculate z.
Calculate the 95%CI for the difference between population means.M Group 1 (Control) 3.50 M Group 2 (Experimental) 3.70 N (pairs of cases) 25 s difference scores 0.25 sMD 0.05
Given the information below, calculate s 2Pooled M S n 050LOT J 1 Group 1 Group 2 96.86 4.50 12 1:CC 106.88 6.40 10
Given N = 18, M = 23.42, s = 5.82, and μ = 25, calculate t.
Here is information about a paired-samples t test. Calculate the 95%CIμDiff.• M1 = 48, M2 = 52• N = 401, df = 400• sD = 14.53, SMD=0.73• tcv = 1.966, t = 5.48
Using the information below, find SM1−M2. Sample 1 n1 = 34 M1 = 26.41 $13.55 Sample 2 n2 = 40 M2 = 32.36 $2 = 5.42
If the 95% confidence interval for the difference between population means ranges from
Given the following, calculate the 95% confidence interval for the difference between population means: M1 = 40, M2 = 50, t = 2.010, and sMD = 2.44.
Given these results, comment on the direction of the difference between the population means: M1 = 28, M2 = 31, t(72) = 7.42, p
Elementary school teachers who did and did not have children of their own were matched in terms of the number of years of experience they had teaching. They were then asked how many minutes of homework a child should complete per night. The researcher planned to use a paired-samples t test to
Paired-samples t tests are more powerful statistically. This means they have a___ probability of being able to reject the null hypothesis if the null hypothesis was false.
A tennis instructor compared two homework methods. She took beginning students at her tennis camp and matched them in pairs in terms of their tennis abilities. She then randomly assigned the players to two conditions. Those in the control condition had to practice for half an hour every day with
Given N = 20, M1 = 68, M2 = 64, and t = 2.01, (a) write the results in APA format and (b) comment on the direction of the difference. Useα = .05, two-tailed.
Given N = 46, M1 =23, M2 = 32, and t = 3.67, (a) write the results in APA format and (b) comment on the direction of the difference. Use a = .05, two-tailed.
Given M1 = 19.98, M2 = 18.65, and sMD = 2.45, calculate t.
Given sD = 8.43 and N = 64, calculate sMD.
Given the following pairs of scores, calculate difference scores: 72 and 75; 69 and 45; 42 and 39; 47 and 46; 55 and 61; 50 and 61; 71 and 69; 55 and 69.
33. The following Venn diagram describes the sample space S of a random experiment and events A, B, and C associated with the experiment. (S consists of 12 elements, denoted by ei=∗i, i = 1, 2, . . . , 12.)A*1*2*10*12*3 *4*5*7 *8 C S*6*11*9 B(a) Express the events A, B, and C in terms of the
32. In Problem 31, construct a bar chart for the probability distribution that satisfies the conditions of a probability distribution.
31. Determine which of the following distributions do not represent a probability distribution.Justify your answer.(a)X = x 0 1 2 3 4 5 p(x) 0.1 0.09 0.2 0.15 0.16 0.2 Review Practice Problems 127(b)X = x 0 1 2 3 4 5 p(x) −0.1 0.09 0.3 0.15 0.16 0.4(c)X = x 0 1 2 3 4 5 p(x) 0.2 0.09 0.2 0.15 0.16
30. Let a random variable be distributed as shown below.X = x 0 1 2 3 4 5 6 p(x) 0.1 0.09 0.2 0.15 0.16 0.2(a) Find the probability p(6).(b) Find the probability P(3 ≤ X ≤ 5).(c) Find the probability P(X ≤ 4).(d) Find the probability P(X >2).
29. A poll was conducted among 1000 registered voters in a metropolitan area asking their position on bringing a casino in that city. The results of the poll are shown in the following table:Sex Percentage of Percentage Percentage not Percentage voters polled favoring casino favoring casino having
28. Suppose that in a bolt manufacturing plant, machines A, B, and C manufacture, respectively, 45%, 25%, and 30% of the bolts. It is observed that the three machines produce, respectively, 5%, 2%, and 3% defective bolts. If the bolts produced by these machines are mixed in a well-mixed lot and
27. Suppose that an insurance company finds that during the past three years, 60% of their policy holders have no accident, 25% had one accident, and the remaining 15%126 3 Elements of Probability had two or more accidents. Further, from their past 10 year history, the insurance company concludes
26. An industry uses three methods M1,M2, and M3 to train their workers. Of all the workers trained, 50% are trained by method M1, 28% by method M2, and the rest, 22%, by method M3. Further 10% of those trained by method M1 do not perform their job well, while 5% trained by method M2 and 15% by
25. Let A1,A2,A3, and A4 be mutually exclusive and exhaustive events in a sample space S, and let P(A1) = 0.2, P(A2) = 0.1, P(A3) = 0.4, and P(A4) = 0.3. Let B be another event in S such that P(B|A1) = 0.4, P(B|A2) = 0.1, P(B|A3) = 0.6, andP(B|A4) =0.2. Find the probabilities P(A1|B), P(A2|B),
24. In a playground, there are 18 players, 11 of them boys and seven are girls. Eight of the boys and three of the girls are soccer players; the rest are basketball players. The name of each player is written on a separate slip, and then these slips are put into an urn. One slip is drawn randomly
23. A bag contains a nickel, quarter, and “dime”, with the dime being a fake coin and having two heads. A coin is chosen at random from the bag and tossed four times in succession. If the result is four heads, what is the probability that the fake dime has been used?
22. Referring to Problem 5, suppose that it takes 11 tests to find all the 10 defectives, that is, the 11th test produces the last defective. What is the probability that the first item is nondefective?
21. Referring to Problem 20, suppose that we are given that the chip selected for the second time is white. What is the probability that the chip selected at the first stage is blue?
20. An urn contains three blue and seven white chips. A chip is selected at random. If the color of the chip selected is white, it is replaced and two more white chips are added to the urn. However, if the chip drawn is blue, it is not replaced and no additional chips are put in the urn. A chip is
19. A certain cancer diagnostic test is 95% accurate on those that do have cancer, and 90% accurate on those that do not have cancer. If 0.5% of the population actually does have cancer, compute the probability that a particular individual has cancer if the test finds that he has cancer.
18. Enrollment data at a certain college shows that 30% of the men and 10% of the women are studying statistics and that the men form 45% of the student body. If a student is selected at random and is found to be studying statistics, determine the probability that the student is a woman.
17. In Problem 16, suppose that a nut is selected at random and is found to be defective.Find the probability that the item was produced by machine A.
16. Three machines A, B, and C produce 40%, 45%, and 15%, respectively, of the total number of nuts produced by a certain factory. The percentages of defective output of these machines are 3%, 6%, and 9%. If a nut is selected at random, find the probability that the item is defective.Review
15. If four addressed letters are inserted into four addressed envelopes at random, what is the probability that(a) No letter is inserted into its own envelope?(b) At least one letter is inserted into its own envelope?
14. A, B, C, and D are four events that are such that P(A) = P(B) = P(C) = P(D) = p1, P(A ∩ B) = P(A ∩ C) = · · · = P(C ∩ D) = p2 P(A ∩ B ∩ C) = P(A ∩ B ∩ D) = P(A ∩ C ∩ D) = P(B ∩ C ∩ D) = p3, P(A ∩ B ∩C ∩ D) = p4. Express the values of the following probabilities in
13. Suppose that six true dice are rolled simultaneously.What is the probability of getting(a) All faces alike?(b) No two faces alike?(c) Only five different faces?
12. Suppose that the probability is 1/365 that a person selected at random was born on any specified day of the year (ignoring persons born on February 29). What is the probability that if r people are randomly selected, no two will have the same birthday?(The smallest value of r for which the
11. In a group of 11 persons, no two persons are of the same age. We are to choose five people at random from this group of 11.(a) What is the probability that the oldest and the youngest persons of the 11 will be among those chosen?(b) What is the probability that the third youngest of the 5
10. The game of craps is played with two ordinary six-sided dice as follows: If the shooter throws 7 or 11, he wins without further throwing; if he throws 2, 3, or 12, he loses without further throwing. If he throws 4, 5, 6, 8, 9, or 10, he must continue throwing until a 7 or the “point” he
9. If the probability is 0.001 that a type-X 20-W bulb will fail in a 10-hour test, what is the probability that a sign constructed from 1000 such bulbs will burn 10 hours:124 3 Elements of Probability(a) With no bulb failures?(b) With one bulb failure?(c) With k bulb failures?
8. Suppose 10 chips are marked 1, 2, . . . , 10, respectively, and put in a hat. If two chips are simultaneously drawn at random, what is the probability that(a) Their difference will be exactly 1?(b) Neither number will exceed 5?(c) Both numbers will be even?(d) At least one of the numbers will be
7. Assume that a given type of aircraft motor will operate eight hours without failure with probability 0.99. Assume that a two-motor plane can fly with at least one motor, that a four-motor plane can fly with at least two motors, and that failure of one motor is independent of the failure of
6. If a lot of 1000 articles has 100 defectives and if a sample of 10 articles is selected at random from the lot, what is the probability that the sample will contain:(a) No defectives?(b) At least one defective?
5. Ten defective items are known to be in a box of 100 items.(a) If they are located by testing the items one at a time until all defectives are found, what is the probability that the 10th (last) defective item is located when the 50th item is tested?(b) What is the probability that if 50 items
4. A “true” icosahedral (Japanese) die has 20 sides, two sides marked with 0, two sides with 1, two sides with 2, . . . , two sides with 9. The probabilities assigned to the 20 faces are all equal. Suppose then that three such dice are thrown. Find the following probabilities:(a) That no two
3. (a) A box of 100 items contains 90 nondefective items, seven with type A defects, five with type B defects, and two with both types of defects. Let S be the sample space generated by the operation of drawing one item blindly from the box. Let EA be the event of getting a type A defective and EB
2. Two inspectors A and B independently inspected the same lot of items. Four percent of the items are actually defective. The results turn out to be as follows: 5% of the items are called defective by A, and 6% of the items are called defective by B. 2% of the items are correctly called defective
1. Certain pieces made by an automatic lathe are subject to three kinds of defects X, Y, Z. A sample of 1000 pieces was inspected with the following results: 2.1% had type X defect, 2.4% had type Y defect, and 2.8% had type Z defect. 0.3% had both type X and type Y defects, 0.4% had both type X and
9. An urn contains five coins of which three are fair, one is two-headed and one is two-tailed. A coin is drawn at random and tossed twice. If a head appears both times, what is the probability that the coin is two-headed?
8. Suppose that in a ball-bearing manufacturing plant four machines M1,M2,M3, and M4 manufacture 36%, 25%, 23%, and 16% of the ball bearings, respectively. It is observed that the four machines produce 2%, 2.5%, 2.6%, and 3% defective ball bearings, respectively. If the ball bearings manufactured
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