Psychology 281 – Final Review Questions
1. In the general population, the Life Stress Scale has a mean of 143.5 and a standard deviation of 23.6. Medical researchers hypothesize that people with high blood pressure are exposed to more Life Stresses than is the general population. To test this hypothesis, they selected 42 patients with high blood pressure and administered the Life Stress Scale.
a) The mean Life Stress score for the high blood pressure sample was 152.6. Can the researchers conclude with .03 that their hypothesis is correct?
b) On the, basis of a second study, the researchers determined that the 94% confidence interval for the mean Life Stress score of high blood pressure people was 144.125 to 156.675. How many subjects were used in this second study?
2. Six students were given a test at the beginning of the school year and again, 3 months later. The purpose of the testing was to assess the extent to which their scores improved as a result of the course work they had done during the 3 months. Their scores on the two tests (each out of 100) are as follows:
First TestSecond Test
72 78
82 80
6568
7475
6968
6674
(a) Perform the appropriate statistical test to see if students' scores improved significantly from the first to the second test (.10).
(b) The same students now underwent a 4-week intensive program of instruction and were then given a third test (also out of 100). Their scores on this test were:
Student: 1 2 3 4 5 6
Third Test: 85 87 76 76 77 82
Is there an overall significant difference in the students' performance on the three tests ( .05)?
3. A western separatist organization claims that Ontario is wealthier because students are better trained and consequently are wore competitive in the job market. An educational psychologist tests this notion by comparing standardized aptitude test scores (LSAT) of Ontario and Saskatchewan university students. The scores of several randomly selected Ontario and Saskatchewan students are listed below:
Ontario SampleSaskatchewan Sample
42.7 33.5
39.338.6
30.5 26.2
36.627.7
38.3 46.0
40.532.3
44.634.5
42.427.0
42.6 28.9
X-bar = 39.722 X-bar = 32.744
s2 = 18.214 s2= 41.238
Test the western separatist organization's hypothesis (.05).
4. Experience has shown that 50 percent of the time, a particular union-management contract negotiation had led to a contract settlement within a 2-week period, 60 percent of the time the union strike fund has been adequate to support a strike, and 30 percent of the time both conditions have been satisfied. What is the probability of a contract settlement given that you know that the union strike fund is adequate to support a strike? Is settlement of a contract within a 2-week period dependent on whether the union strike fund is adequate to support a strike?
5. To determine whether the location of a brain injury in the left hemisphere was related to language dysfunction, researchers measured language production ability in 90 patients. The number of patients scoring above average and below average on the test is presented in the following table as a function of the location of the injury.
Score
Injury Location Below Above
Left Anterior 16 6
Left Temporal 15 18
Left Parietal 17 18
a) Do these results warrant the conclusion that classification as above or below average on the test of verbal production is related to location of injury? (.05)
b) In the general population) the anterior, temporal, and parietal areas account for 40%, 23% and 37% of the relevant area of the brain. Do the results in the preceding table permit the researchers to conclude that the probability of an injury in the different locations depends on more than simply the size of the different brain areas? (.05)
6. According to legend, the beaches in the fantasy kingdom of Loof Lirpa are lined with precious stones, specifically, diamonds, rubies and sapphires. While on vacation there you combed the beaches and found 6 diamonds, 7 rubies and 3 sapphires. Unfortunately, getting them out of the country is another story. When you arrive at the airport you find your cab fare is 6 precious stones. How many ways to pay it are there if:
a)your payment must include at least two diamonds?
b) you decide to pay with three diamonds, two rubies and one sapphire?
You now have 3 diamonds, 5 rubies and 2 sapphires. Unfortunately, the guy who collects the airplane boarding tax also demands a precious stone in payment and randomly selects one from your bag. If this man receives a diamond, he will let you board the plane immediately, however, if he receives anything else there is a 50:50 chance he'll send you to the emigration desk.
c) What is the probability that he allows you to board the plane?
d) Given that he allowed you to board the plane, what is the probability that he selected a diamond from your bag?
7. A box contains 5 red chips and 3 blue chips. You are to draw a chip at random, without replacement, until the first blue chip is drawn. Let the random variable X denote the number of draws.
a) Find the probability distribution of X.
b) Find the mean of this distribution.
c) Find the variance of this distribution.
8. Of the customers who do business at a rental car agency, 20% prefer large automobiles.
a) In a randomly selected group of 15 customers what is the probability that at least 3 of the customers prefer large automobiles?
b) In a randomly selected group of 100 customers what is the probability that between 16 and 26 (inclusive) of the customers prefer large automobiles?
c) What is the minimal number of large automobiles the agency should have on hand to ensure, with a probability of at least 0.9, that it can meet the large automobile demand of a randomly selected group of 225 customers?
9. An experimenter is interested in determining the effects of shock on the time required to solve a set of difficult problems. Subjects are randomly assigned to four experimental conditions. Subjects in Group 1 receive no shock; Group 2, very low-intensity shock; Group 3, medium-intensity shock; and Group 4, high-intensity shock. There are 12 subjects assigned to each condition. The means for the different groups are 9.25, 7.33, 13.0, and 16.25 for Groups 1, 2, 3, and 4, respectively. Further, when each raw score is squared and these squared values are added together the sum is 7434. Is there a significant (.05) difference among the four groups? If possible, do post-hoc pair-wise comparisons (Newman-Keul) at .05.
10. It is known that the mean number of errors made on a particular pursuit rotor task is 60.9. A physiologist wishes to know if persons that have had spinal cord injury, but who are now "apparently" recovered, perform less well on this task. In order to test this, a random sample of 8 persons that had spinal cord injuries is taken and administered the pursuit rotor task. The number of errors made by each subject is shown below.
63, 66, 65, 62, 60, 68, 66, 64
a) Is there evidence to believe that "recovered" patients are impaired in performing the task? (.01)
b) Form the 90% confidence interval for the mean.
11. The Acme company produces flashlight batteries that have a true mean lifetime of 21.4 months and a standard deviation of 1.2 months. The Apex company produces flashlight batteries with a true mean lifetime of 25.5 months and a standard deviation of 1.8 months. A random sample of 50 flashlight batteries from Apex is taken and a random sample of 70 batteries from Acme is taken. What is the probability that the difference between the mean lifetimes of these two samples will exceed 4.5 months?
12. A random numbers table of 250 digits showed the following distribution of the digits 0, 1, 2,...,9. Does the observed distribution differ significantly from the expected distribution? ( .05)
Digit: 0 1 2 3 4 5 6 7 8 9
Observedfrequency: 17 31 29 18 14 2035 30 20 36
13. A drug company has developed a new analgesic drug (for pain relief) which seems to be very potent at very low doses. This drug is tested at two different doses along with a placebo on separate groups of subjects. The subjects' pain thresholds are measured by recording reaction time to a mildly painful stimulus. The deviations from the mean reaction time for each group aregiven in the table below:
Placebo 1 mg10 mg
-1.2 0.5 1.1
2.3 1.6-2.0
1.6-2.1 0.7
-2.1 2.4-1.6
-1.8-1.7 2.2
2.0-0.9 0.2
-0.8 1.3 1.0
-0.8-1.6
-0.3
The mean reaction times for the three groups were 18.1 sec, 22.0 sec., and 29.8 sec respectively.
a)Is there a significant analgesic effect of the drug treatment? (Use .01)
b) Do Newman-Keul's multiple comparisons to determine which groups differ significantly. (Use .05)
14. There was once a man who had two sons he loved equally. The man wished for both sons to become doctors, but he knew that the first son was not as bright as the second. In the first term of medical school the first son only passed 45% of the tests, while the second son passed 80% of the tests. The father then determined that he could not support both sons in the second term of medical school, but because he loved them equally he randomly selected one to continue. Assuming that the sons would perform at the same level they showed in the first term, answer the following:
a) What is the probability that the chosen son failed the first test of the second term?
b) If we know that the son passed the first test of the second term, what is the probability that this was the first (less bright) son?
15. A large car rental agency sells its cars after using them for a year. Among the records for each car are mileage and maintenance costs for the year. To evaluate the performance of a particular car model in terms of maintenance costs, the agency wants to use a 95% confidence interval to estimate the increase in costs for each additional 1000 miles driven. Use the following data to accomplish this objective:
CarMiles Driven (in 1000s)Costs
1 54 326
2 27 159
3 29 202
4 32 200
5 28 181
6 36 217
16. When mice are subjected to stress their endogenous opioid system is activated and the mice increase food consumption in the post-stress period. To test if a loud noise (85 db) is a stressful stimulus, we expose 10 mice to the loud noise for 1 hour and expose 8 mice to normal room noise levels. We measure their food consumption over the next two hours and obtain the following data:
Loud noiseNormal noise
1.050.60
0.800.80
1.150.75
0.250.65
1.600.70
0.300.60
0.950.55
1.850.85
0.55
1.00
Do these data suggest that the loud noise activated the opioid system and increased food consumption? ( .05)
17. The provincial government is currently investigating the issue of underfunding in universities. They have data which indicate that North American universities spend $10,000 on each student, on average, with a standard deviation of $1500. They also have data. indicating that student personal income averages $9,000 per year, with a standard deviation of $3000. (Both expenses to universities and incomes of students are normally distributed.) They decide to survey 8 Ontario universities and 1000 students. Government funding will only be raised if the average student income is below $8,900 and average university expenses are above $10,100. What is the probability of this event?
18. Is there a significant difference between the Psychology 281 grades earned by students from different faculties? To address this question, the Psychology 281 final exam scores of a random sample of 40 Social Science students were compared to those of 50 Science students. The means and variances of these scores are as follows:
Social ScienceScience
n = 40 n = 50
X-bar = 70.5 X-bar = 72.1
s2= 200s2 = 250
a) Determine whether a significant difference exists between the mean scores of these samples ( .05).
b) Suppose that, in fact, the mean final exam scores of the populations of Social Science and Science students differ by 3 points. Given this, what is the probability that you would fail to detect a significant difference based on the sample sizes and variances used in part 'a' (still using .05)?
19.Certain dosages of a new drug developed to reduce a smoker's reliance on tobacco may reduce one's pulse rate to dangerously low levels. To investigate the drug's effect on pulse rate, different dosages of the drugs were administered to 6 randomly selected patients, and 30 minutes later the decrease in pulse rate was recorded.
PatientDosageDecrease in pulse rate
1 2.0 15
2 1.5 9
3 3.0 18
42.516
54.023
6 3.0 20
a) Is there evidence of a linear association between drug dosage and change in pulse rate at the .10 level?
b) What is the predicted decrease in pulse rate for a person receiving a dosage of 3.5, and what are the 99% bounds to the error of this prediction?
20.Santa keeps a record of the weights of packages he loads on his sled. In past years, the weights of the packages have been normally distributed with a mean of 9.0 kg and a variance of 6.25.
a)Santa wants to make sure Rudolf and the team can pull the sled. If Rudolf and the team can only pull the sled if the total package load does not exceed 2000 kg and Santa puts a random sample of 233 packages on the sled, what is the probability that Rudolf and the team won't be able to pull it?
b)This year Santa suspects that the packages are lighter than usual. A random sample of 20 packages has a mean weight of 8.5 kg. Are his suspicions correct? (.05)
c)Assume that Santa doesn't know what his mean package weight over the years has been. On the basis of this year's information, create a 99% confidence interval for the true mean package weight.
21. Nausea is a common symptom among postoperative patients. A group of physicians are interested in comparing two new drugs, A and B, for their effectiveness in preventing postoperative nausea. One hundred and eighty patients scheduled for surgery were used in the study, with 60 assigned to receive each drug or a placebo. After surgery, each patient was classified according to the degree of nausea he reported. The results are as follows: do they indicate a difference between the drugs and the placebo in terms of their effect on nausea? ( .05)
DEGREE OF NAUSEA
None Slight Moderate High
DrugA 40 10 6 4
DrugB 36 12 4 8
Placebo 30 16 8 6
22. The mean IQ of all female students at UWO is 112 with a variance of64. The mean height of all male students at UWO is 68 inches with a standard deviation of 3.4 inches.
a)What is the probability that a female student chosen at random at UWO has an IQ between 107 and 116?
b)What is the probability that a male student chosen at random from UWO will be shorter than 64 or taller than 70 inches?
c)If you observe a couple on a date (assume there is a female and a male), both of whom are UWO students, what is the probability that the woman has an IQ of greater than 100 and the man is shorter than 74 inches?
23.Because of the acid rain problem, there is a small lake in northern Ontario which has only 8 fish left: 4 trout and 4 pike. Suppose you decide to go fishing in the lake one day and plan to stop as soon as you catch the first trout.
a) Create the probability distribution for the total number of fish you will return with assuming you keep all the fish you catch.
b) Below is the probability distribution for the number of fish caught if you decide to stay out until you catch 2 trout. What are the mean and variance of this distribution?
x p(x)
2.2143
3.2857
4.2572
5.1714
6.0714
24. Researchers wanted to determine the kinds of people who visited the LondonArtGallery. They asked 400 visitors their residence (London, Other Ontario, or Not Ontario) and their ages, which were classified as young (Y: m ore than 1 standard deviation below the mean), somewhat young (SY: between -l standard deviations and the mean), somewhat old (SO : between the mean and +1 standard deviations), and old (0: more than 1 standard deviation above the mean). The results are presented in the following table.
Age
Y SY SO O
London8 46 65 41
OtherOntario124348 27
Not Ontario204137 12
a) Is there a significant relationship between the residence of people and their ages, with .10?
b)Does the LondonArtGallery attract more people from one of the three residence areas than from another, ignoring age?( .05)
c)Does it appear that the distribution of the ages of visitors from London fits a normal distribution? ( .05)
25. One of the ways of assessing the quality of a university is in terms of the amount of research funds the faculty bring to the university. An administrator at WarthogUniversity knows that, historically, Warthog professors have brought in an average of $5870 per person in research funds, with a standard deviation of 550. She also knows that professors at arch-rival BisonUniversity have attracted an average of $3925 per person, with a variance of 245025. Concerned that Bison may be catching up to Warthog, the administrator takes a sample of 44 Warthog professors and 39 Bison professors and records their grant amounts for the most recent year.
a) Assuming that the means and variances have not changed, what is the probability that in these samples the Warthog mean exceeds the Bison mean by at least $2000?
b) The administrator suspects that the difference between Warthog and Bison professors has narrowed because of recent hiring at Bison. If, in fact, the true difference is now $1550, what is the probability that the administrator detects that the difference is narrowing when she samples 50 faculty from each university? ( = .05)
26. Simple reaction times to green, red and yellow instrument panel lights were compared. The three light colours were randomly assigned to 31 different subjects who were instructed to press a button in response to the light. The data below are average reaction times (in milliseconds) for the 31 subjects.
a) Is there an overall difference among the light conditions? ( = .01)
GreenRedYellow
mean 201 215 218
variance 2.9 3.5 3.4
ni 10 11 10
b) Due to the fact that “green” means “go” when driving, prior to running this experiment, the researchers expected that green lights would be responded to faster than red lights. Is this expectation borne out by the results? ( = .05)
27. Rawlings, one of the companies that makes baseball uniforms, has noticed that 45% of their customers request blue lettering, 35% request red lettering and 20% request some other colour. Among those requesting blue lettering, 60% also request player numbers on the sleeves while only 40% of the other customers do.
a) What is the probability that the next order Rawlings receives will not be one requesting player numbers on the sleeves?
b) If the next order does request player numbers on the sleeves, what is the probability that it is an order for red lettering?
c) In the past year, there have been exactly 50 orders. Twenty have been for blue lettering (14 with numbers on the sleeves), 15 have been for red lettering (8 with numbers on the sleeves) and 15 have been for green lettering (5 with numbers on the sleeves). If Rawlings randomly selects 10 of these uniforms to put into their brochure, what is the probability that they select no more than 1 green uniform?