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Statistics For The Behavioral Sciences 8th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions

5. Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research(Peresson, Bringlov, Nilsson, & Nyberg, 2004), In a typical study, a researcher obtains
4. If the alpha level is changed from u - 05 to @ - 01.a. What happens to the boundaries for the critical region"b. What happens to the probability of a Type I error?
3. In wonls define the alpha level and the critical region for a hypodsctis Jest.
2. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuring that all other variables are held constant, explain how the val of is influenced by each of the following:a. Increasing the difference between the sample mean and the original popolation meanb.
1. In the z-score formula as it is used in a hypothesis test.a. Explain what is measured by M in the numeratorb. Explain what is measured by the standlieder in the denominator
23. Welsh. Duvis, Burke, and Williams (2002) conducted a study to evaluate the effectiveness of carboloydinte-electmilyte drinic on spurts performance and endurance Experienced athletes were given either a carbohydrate-electrolyte drink or a placeto while they were tested on a series of
5. Is it reasonable to conclude that this set of n - 16:people is not a representative random sample of registered voters?
22. People are selected in serve on juries by randomly picking names from the list of registered voters. The average nge for registered voters in the country is w - 39,7 years with a standard deviation of o - 12.4 A statistician randomly selects a sample of a = 16 people who are currently serving
21. The average age for licensed drivers'in the county is- 42.6 years with a standard deviation of or - 12.The distribution is approximately normal A researcher obtained a sample of n = 36 drivers who received parking tickets. The average age for these drivers was id = 40.7. Is this a reasonable
20, A normal-shaped distribungo has (L = 80) and @ - 15a. Sketch the distribution of sample means for sam-ples of # = 25 vores from this population.b. What are the score values that form the hound-imiev for the middle 95G of the distribution of Azonple means?G Compiute the z-scure for M | 89 har a
19. A random cumple of w = 4 cores is selected from ul normal population with a men of [ = 90) and a standard deviacion of o - 12.IL. What is the probability that the sample mean Is between MM = 87 md M = 931b. What's the probability that the sample mean iv between M - 51 amt M - 967e. What is the
IN. The population of SAT scores forma a harmal`distribution with a mean of p = 5(KI and a standard deviation of a = 100. If the average SAT score is calculmed for a sample of # - 25 students,.. What is the probability that the saanple men will be greater than M = 5.10. In symbole, what isb. What
17. A population of scores forms à normal distribution With a metal of a = Bland a standard deviationa. What proportion of the scores have yalies between 75 and 832 h. For samples of it - 4, whit proportion of the samples will have mrun between 75 and 85?c. For samples of n = to. what proportion
2. What is the probability of randomly selecting u.score less than X = 347 What is the probability of selecting a sample of n = 9 scores with a mean less than M - 342c. What is the probability of selecting a cumple of I = 30 scores with a mean lese ihon'M = 347
16. A population of scores forms a normal distribution with a meta af p = 40 and a standard deviation of or - 12.
. If samples of mr - 16 are selected from the population. what proportion of the samples will have menne less than M = 807
15. A population of scores forme a normal distribution with a mean of u = 75 sind a standard deviation of₪ -20.# What proportion of the scores in the population have-values less than X = ROYb. If samples of n = 4 are selected trees the population, whid proportion of the samples afil have meine
14. The population of IQ scores forms a normal distribution with a mean of a = 100 and sitindard deviation of it - 15. What is the probability of obuaning a sample mean greater than Af ~ 105.a. for a midom sample of a = 9 people !!b. for a random sample of n = 36 people?
13. A normally distributed population has a mean of= 80 and a suandard iteviation of u = 20. Calculate the z-score for cach of the following samples, Based on the z scure value, determine whether the sample mean is a typical, representative value oe an extreme valus for samples of this size.a. A
12. A random sample is obtained fruin a population with i mean of It - 50 and i standard deviation af d -12. For a sample of it = 4 scorek, would a sangue mean of M - 55 be considered an extreme value or is it a fairly typical sample mean?h. For a sample of n = 36 scores, would a sample meil of M =
11. A sample of n = 25 scores, luis a mean of M - 84,3 Find the +-score for this samplea. If it was obtained from a population with L = RO and or - 10.h. If it was obtained from a population with w - 80e. If it was obtained from a population with a = 80 and o = 40k
10. For a population with a man of | - 60 and a standard deviation of or - 24, find the 2-score corresponding to each of the following samples.IL M 63 for a sample of n - 16 3cores h. M - 63 for a sample of # - 36 spares;e. M - 63 for a sample of a = 04 scores
9. For n sample of n = 16 scoret, what is the value of the populatico standard deviation (o') in order to have a Standard ermDe od Il. 04F = 10 polis?la. W - 5 pracnis?C. w - 2 points?
8. If the population standard deviation is o - 8, how large a sample is necessary to have a standard ciroe that isa. less than 4 points?b. less than 2 points?C. Jess than 1 point?
7. For a population with a standard deviation of o - 10.how large a sample is necessary to have a standard emur that is:a. less than or equal 10 5 points?b. less than or equal to 2 points?e. less than or equal to 1 point?
6. For a population with a mean of L = 50 and a standard deviation of o = 10, how much error, on average, would you expect between the sample meun(M) and the populutice mean for;D. a sample of mr - 4 Scoresb. a sample of w - 16 scorese. a sample of a = 25 scores
5, A randoma simple is obtained from a population with a mean of | - 100 and a standard deviation of @ = 20a. How much error would you expect between the saniple mean and the population mean for a sample of w = 4 scores ?.b. Hover mach error would you expect for a sample of # = 16 scores?e. How
4. The distribution of sample means is not always a normal distribution. Under what circumstances will the distribution of sample meses nor be normal?
3. A sample is selected from a population with a mean of 4 - 80 and a standard deviation of or = 20.a. What is the expected value of M sed the standard error of M for a sample of n = 4 wcoros?b. What is the expected value of M and the standard error of M for a sample of n - 16 scores?
2. Describe the distribution of sample means (shape, expected value, and standard error) for samples of# # 36 selected from a population with a mean of== 100 and a standard deviation of a - 12
1. Briefly define each of the following!a. Distribution of sample meansb. Expected value of Mc. Standard error of M
28. 4 dischse affech 10% of the Individual in a population und a sample of 100 penple is selecteit Itutu the population.a. What is the probability of finding the disease in un leist 33 scopie? (Be careful "At least 15" mennieb. What & the probability of Finding the disease in fewer than 3 people.
27. For a balanced coli,a. What is the probability of velting more than 30b. What is the probuhillay of getting more thim 60 heads in 100 14ses?c, Purta a zad o both asked for the probability of geding more than otH55 hende in a series of coin losses ( -605) Why do you think die two probabilities
&. How many heads would you expect yo get unb, What is the probability of getting more than 50 heade!4. What is the probability of getting micily 50 heads?
25. Che test for ESP involves using Zener cund Fach card shows one of fire different symbole (sipuare circle, star, cross, wary lincs), and the person being Irsicd has to predict the shape of cach cand before i in selected, Find each of the probabilities requested for a person who has mi ESP and is
24. A true-false test has 30 questions. If a passing prode on this Test \\ X = 24 (or moee) correct, what is the probability of obtaining a pissing grade jour by.guessing!
23. A true/false test has 50 questions, If a students is sitt ply guessing at the answerh,a. What is the probability of guessing correctly for any question?h. On average, how many questions would a student get correct for the entice Inst"!c. What is the probability that a student would get more
22. A multiple-choice test has 48 questions, cach with four response choices, If u student is simply guessing at thea. What is the probability of guesung correcily for any question?h. On average, how many questions would u statem get comeet for the entire tien?e, What is the probability that a
21. Laboratory mats commit an average of |= = 40 errors before they sulve a standardized mace problem The distribution of error scores is approximately normal with n standard deviation of ar = 8. A researcher is testing the effect of a new dietary supplement un intelligence, A newborn mat is
20. A consumer survey indicates that the average household spends ( = $155 on groceries each week The distribution of spending amounts is approximately pormal with a standard deviation of o = $25. Based on this distribution.a. What proportion of the population spends mnice than SE75 per week ou
19. Information from the Department of Motor Vehicles indicates that the average age of heerocif drivers is u - 39.7 years with a standard deviation of q - 12.5 year. Assuming that the distribution of deivers' ages is approximately normal,#. What proportion of licensed drivers are more than 50
18. A normal dismibution has a mean of | - 80 and a standard deviation of + = 10; For each of the following scores, indicmic whether the body of the distribution is to the left of right of the score, and find the penportion of the distribution in the body E X - 78d. X - 71
17. A normal distribution has a mere of w - 60 and a'standard deviation of a ~ 20. For each of the following screes, indicate whether the tail of the distribution is to the left or tight of the sobee, said find the peuportion of the distribution in the taila. X = 75 h. K = 65 CX - 50d. X - 30
16. The diunibution of SAT scores is noemal woth M - 500 aml (r = 100a. What SAT scom; X value, separates the top 15% of the distributicin Troen the fest!b. What 5AT score, X value, separmes the ip 20% of the distribution from the rest?- What SAT score, X value, separates the top 25% of Ibe
15. The distribution of scores on the SAT is approximately normal with a mean of p = 500 and a statdard deviation of g = 100, For the population of students who have taken the SAT.h. What proportion have SAT scores greater than 7007b. What propicetico have SAT scores greater than 5509 C. What is
14. The distribution of IQ scores la normal with p = 100 and o - 15. What proportion of the population hal IQa. Greater than 1157 be Greater than 1307 2. Greater shan 1457
13. A normal distribution has A mean of L = 50 and a standard deviation of o - 12. For each of the following scores, indicate whether the tail is to the night or left of the score and find the proportion of the distribution located in the tail.1. X -53b. X = 44e. N = 68d. x = 38
12. For a normal distribution, find the E-score values that separatea. The middle 609 of the distribution from the 404 in the tailsb. The middle 70% of the distribution from the 30%in the taillis,e. The middle 80ft of the distribution from the 209 in the tailsd, The middle 90% of the distribution
11. What proportion of a normal distribution is located a: Between : - 11.50 and= - 0.50b. Between z - 100 and z = - 1.00.e. Between : 0 und z - - 1.50.4. Between = = 1.75 and == - 11.25.
10. Foca normal distribution, identify the z-score location that would separate the distribution into two sections so that there isa. 70% in the body on the right hand sideb. 80% in the body on the right-hand tile 6. 75% in the body on the left-hand skle.d. 90% in the body. on the left hand side
9. For a normal distribution, identity the z-sceee location that would separate the chatribution into two sections so than there is a+ 1095 in the tail on the right-hand side:b. 20% in the mail on the right-hand side.e. 20% in the mail on the left hand side.d. 30% in the tail de the left-hand side.
8. Find eoch of the following probabilities for a normal 1. PC-1.00)
7. Find esch of the following probabilities for a normista. PL: > 1.00)b. plg 2: 0.80Y CMS (25)d. ptE ≤ 1358
fr. For each of the following a scores, sketch a normal distribution and draw a vertical line at the location of the soon. Then, determine whether the body is to the right on the left of the lioe uni find the propomop in the body 2. 2 =0.75 LI=0.85d. : - - 2.10
5. For each of the following > scores, cheich a normal distribution and draw a Vertical line at the location of the zysoon. Then, determine whether the tall is in the right of the left of the lice and find the proportion in de tall A. 24 1:50b. z= - 1.75 CZ-0.20d. : - - 0.50
4. What is sumpling with replacement, and why wat uved!
3. What requirements must be satisfied so have u min
2. A kindergarten class consists of 14 bays and 1 1 girfs.If the teacher selects children from the clans usta Fandom somplinga. What is the probability that the first child selected will be a girl?h. If the tencher selecis a rundum cumple of n " ]children and the first two children are boch boys,
1. A jar contains 20 ved marbles of which 10 are large and 10) ure small, and 30 blue marbles, of which 10 are large and 20 are small. If 1 marble is randomly selected from the jar.1. What is the probability of obtaining a blue marble ?.b. What is the probability of obtaining a large machle?e, What
. The following sample of n - 6 scores has a mean of M - 6 and a standard deviation of $ 4, Scoresr 10, 0, 4.8,4, and 10.H. Find the E-score for each X value.b. For the sample of N = 6 7-scones, verify that the mean is zero and the standard deviation is I.
28. A population consists of the following N = 5 scoree 0.6.4. 3. med 12.. Compute ; and if for the population.Jb. Find the = score for each socee in the population.c. Transform the original population into a new population of N = 5 xcomes with a renn of #t = 60 and a standard deviation of o = 8.
27. A populmion consists of the following NV = 0 xcores;6. 1. 3. 4, 7, amd 3.u. Compute j and ir for the populatiti.b. Find the @score for each score in the population.c. Transform the original population into a new popalation of N = 6 scores with a men of it = 50 and a standard deviation of q = 10
26, A distribution with a mein of y = 38 and a standard deviation of ir - 20 is being transformed into a standardized distribution with w - 50 und or - 10.Find the new, standardized score for each of the following values from the original peputation 1. X 48b. X= 40 4. X =30 4. X - 18
25. A distribucion with a mean of | - 6id und'a stundard deviation of o = 4 is being wasformed in a standardized distribution with p = 100 and o -20 Find the new, standardized score fue each of the following values from the original population 8. X = 00b. X =32.CX-32d. X = 66
24. Which of the following exam scores shoold lead to the better grade?a. A score of X = 55 on an exam with p = fil) andb. A.score of X = 40 on an exam with = = 50 and 0 =20.Explain your answer
2.3. Which of the following exam scores should lead to the better grade?u. A score of X - 43 on an exam with p - 40 and₪F - 2.b. A score of X = 60 co an exam with 4 = 50 and₾=20 Explain your answer
22. Suppose that you have a score of X = 75 on an exam with a - 80. Which standard deviation would give you a better grade; or - 2 or or - 107
21. Suppose that you have a score of X = 75 on an exam with a - 78, Which standard deviation would give you a better grader or - Para - 102
20. For each of the following populations, would a score of X = So he considered a central score (near the middle of the distribution) or an extreme yenre (tar out in the tail of the distributiony?R. 4 = 45 and o = 10b. p - 40 and o - 2 6 - 55 and-o -d. p = 60 indo = 20
19. In a distribution of scores, X - 62 corresponds 10= +0.50, und X = 52 corresponth in -2,00. Find the mean und stickbird deviatinn for the distributim
IN. In a population of exam scores, a score of X = %(unresponds to === +1.00 and a score of X =79 ogresponds to 2 - 1.00. Find the meat and standard devision for the population. (Alar. Skeich the
17. For a population with a mem od p - 70, a scuve. of=04 corresponds to > = "2.00 What is the population standard deviation?"
X . 90 corresponds tisz - 0,50. What is the sample standard deviation?
15- For a sample with a stanilant deviation of =6,4 store of X -65 corresponds to = - 1:50: What is the sample mean ?!
14. For a population with a standard dessaton of o = 10, a scare of X = 44 comesponds to = = - 1.50. What is the population moon?
1.3. A scure that i 4 points above the mesn corresponds to a Escoge of == 0,50. What is the populicion standand deviation"
12. A score that is 0 points helcro the mean conespeeds 2.00. What is the population standard deviation?
1.1. Find the X value corresponding po 7 - 1.50 for euch of the following distributions-400=b. w - 40 do- 20& -80 and o - 4d. p=30 and o = 8
10. Plnil the 55cone coeresponding to a shore of N = 60 fot cach of the folloutog distribution C. JE = 70 and o - 20
A sample has a mean of M = Ull and a standard deviation of . - 5. For this sample, find the X valus corresponding to each of the following cscones.2=0.80£= 1.20 E=2:00== 0.40= 1.60 ==- 1,80
. A sample has a mean of M - 40 and u standaril devintion of a = 4. Find the a solite for each of the following X values from this kumple X-44 X=42 X = 48 X == X=50 X=46
7. A population has a mean of p = 40 pad a standard deviation of IF - 11 IL. For this population, find the z-score for each of the following X values.¥=43 X-49 X-52 X=34 X=28 X= 64 h. For the same population, find the score (X value)that corresponds hir each of the following escores z-0.75==
6. For a population with a mean of p = 100 and a standard deviacion of o LO,a. Find the &score for each of the following X valiles X-105 X-120 X-130 X=90 X=85 X=60b. Find the score (X value) sha comresponds in each uf the following 2-scores z =- 1,00 == 0.50 == 2.00[= 170 2 = 1.50₹ =- 1:50
5. For a population wich |A = 60 and o = 9, find the-score for each of the following & values. Nole: You probably will need to use a formula und a calculator to find these values Y X - 65 X-70 X-53 X-48 X-75 X-58
4. For a population with it - 50 and o = 10a. Find the score for ench of the following X values:Wane, You should be able to find these values using the definition of n ?- score, You should not need to use u formala of do any seriouk calculations J X - 55 X= 60 X = 75 x=45 X=30 *= 35b. Find the
3. A distribution has a standard deviation of -4 Describe the location of each of the following-scores in terms of its position relative to the mean. For example, +1.00) is a location that is 4 points above the moan a2+2.00b. +0.50 ez--2.00 d=-0.50
2. A distribution has a standard deviation of a = %. Fisd the =score For each of the following locations in the distribution.B. Above the mean by 4 pointsb. Above the menn by 16 point !!e. Below the mean by & points.d. Below the mean by 12 points
1. Whuid information is provided by the sign ( +/- ) of a-score? What informatica as provided by the memberical value of the z-soome?
29. In the Preview section at the beginning of this chapter, we discussed a study by Wegerin and Steen (2004) that.reported greater consistency (less variability) in memory scores for younger women than for older wownen. The following data represent spoees for two women, one older and one younger,
28. In an extensive sandy involving thousands of British children, Arden and Plomin (2006) found significantly higher variance in the intelligence scores for males than for females. Following are hypothetical data, similar to the results obtained in the study. Note that the scores are not regular
27. Caleulane SS variance, and standard deviation fur the following sample ofN = 8 scons 0. 1, 0,3, 6.0.2/01(Note The computational formula for 55 works bed with cheser scures, 1
26, Calculate SS, variance, and standard deviation for the following saniple of Il = 4 scores 3. 1. 1, 1(Note: The computational forminla worldchesk with these scores.y
25. Caleulise SS. carinode: nad taadund deviation for the following sample of it - 4 somes, 450. 1. I. (Note:The computational formula for SS works well with these scorer.)"
24. Calculate 55. varimey, and ijimdird deization for the following sample of n - 5 30000 10.3, 8. 0.4(None The definitionat furmula works well with
23. Culcalme SS, varinoce, and standard deviation for the.following sample of in soorec 11, 0, 8, 2,4,5 INone The delmitional Formula for 55 wocks well with these score.V
22. For the Illoving sample of n = Tacutee.12. 1. 10. 0. 3. 3. 7. Sketch a histogramtt showing the sample distribution, h. Locate the value of the sanmle mean in your skrich, and make an estimate of the standard deviation (as done in Example 4.5).c. Computo SS, variance, and standard dexsation for
21. For the Following population"\( N = 6 scentsa. Sketch a histogram sebring the populationb. Locale the value of the population meun in your Skinicht and make an qstimare of the shammilord deviation tas done in Eample 4,2)e. Compute SS, variande, and standard deviation for"""the population. (How
20. For the following population of N = 10 xcom HL 6. 3. 3. 13, 8, 9. 12. 1. 0 me Skisch a histogram sbirine the population dutributionsb. Lachie the value of the population mein is your skmich anil make an esumme of the standund deviation li done in Example 4/2)c. Compiac SS, variance, pod
19. For the following population of N = 6 sounes ..8. 6. 1. 6 1 5 n. Sketch a histogram showing the population.distributionb. Locate the value of the population ment in your sketch, and make in estimate of the standard deviation (as done in Example #2%c. Campore 55, variance, and stamiliard
Calculate the mean for each of the following sample and then decide (yes or no) whether if would be chs to use the definitional fornala to calculate the valod Sample A Sample B: 3. 0. 9. 4 17. For the following scurese 3. 2. 5. 0, 1, 2, H Calculate the menn. INcee that the value of the mean does

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