Review for Cumulative Final Exam
1. / The following is known about test scores obtained by 30 students in a Statistics course:
x = 2220
x2 = 173586
a. Approximately how many people obtained a score between 80 and 90?
b. If lower than 65 is a failing grade, how many people failed?
c. If only the top 10% of scores receive As, what is the lowest score required in order to still get an A?
d. What proportion of individuals obtained a score between 65 and 80?
2. / The following is known about 10 students’ pupil diameters (in mm) and their GPA:
r = .80
Mean / Standard deviation
pupil / 8 / 1.7
GPA / 2.4 / .4
- Predict the GPA of a student whose pupil diameter is 8.85mm:
- Predict the pupil diameter of a 4.0 GPA student:
3. / You conduct a study of the effects of the new drug -glutraine on human memory. You test a sample of 30 participants in your FDA approved laboratory on standard memory tests that provides a performance score for each participant on a scale of 1 to 10. Where the score indicates the number of items recalled (out of a total ten words). You divide 30 particpants into three groups of 10. The first group receives and sugar pill one hour before tests; the second group receives a small dose of -glutraine; and the third group receives a large dose of -glutraine. Once 1 hour after an-glutraine pill has been swallowed by each participant the participant is given ten minutes to memorize a 10-word written passage from a novel. One hour later each subject is tested on his or her memory performance (use alpha=.05).
Sugar pill / Low dose / High dose
3
2
5
4
3
1
2
4
5
6 / 1
2
1
1
4
1
9
10
1
2 / 7
8
7
9
8
9
9
9
7
9
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. What is the appropriate statistical test?
d. Calculate the test statistic:
e. Make a decision, what does it mean?
f. If you had a patient suffering from memory loss, which dose would you recommend to them based on this analysis and why?
4. / I would like to evaluate whether my cat is psychic. I present her with 4 treats simultaneously where each treat is accompanied by a photo of a racehorse. I then record which treat she eats first and use this information to place a bet on a horse race in which these 4 horses are competing. I do this 14 times.
- What is the probability she will guess the winner of all 14 races?
- What is the probability she will guess the winner of at least 10 of the 14 races?
- What is the probability she will guess the winner of at least 8 races out of 14 if 5 horses were competing (and I gave her 5 treats to choose from?
- What is the probability she will guess the winner of all 14 races if only two horses compete (and I only put two treats in front of her)?
5. / A social psychologist believes that we should eliminate the drinking age requirement because it may promote excessive binge drinking on individuals’ 21st birthdays. She asks 5 people to report the number of servings of alcohol they consumed on their 21st birthday celebration, and a totally different group of 5 people to report how many servings they consumed on 22nd birthday. Test the hypothesis that the number of drinks consumed on a 21st birthday is different from the number consumed on a 22nd birthday (use alpha=.01).
21st B-day / 22nd B-day
9 / 3
4 / 1
12 / 7
11 / 9
10 / 0
- What is the appropriate test?
- State the null hypothesis:
- State the alternative hypothesis:
- Find the critical value:
- Calculate the obtained statistic:
- Make a decision:
- What does your decision mean?
- Use SPSS to perform this same analysis and confirm the same result. Paste your output below:
6. / The following is known about a set of 5 sample test scores:
x = 34
x2 = 396
- Find the Sum of Squares (SS):
- Find the standard deviation:
- Find the standard error:
- Find the variance:
7. / A prominent university requires all applicants to take a standardized test in order to qualify for admission to their Psychology program. The school accepts only the students who received scores in the top 13% of that year’s distribution. The following is known about the 2012 group (which contained a total of 15 students):
x = 1154
x2=91452
In 2012, the following are 5 of the students who applied to the program (along with their respective grades}:
Sawyer = 77
Jack = 89
John = 96
Kate = 95
Claire = 93
a. Who gets in under the current acceptance policy?
b. Who gets in if the top 24% are admitted?
8. / You are in charge of NASA’s astronaut engineering program, which sends engineers into space to fix broken satellites. You typically sent a team of 2 people, 1 male and 1 female to repair the two most crucial components of the structure: the fuel tank and the rocket motor. The repairs must be as quick as possible, and you are in charge of assigning a specific job to your male and female engineers. Below is data from 20 past male and female engineers and the time it took for them to repair both of the component types (in seconds).
Fuel Tank / Rocket Motor
Male / 3
3
1
3
2 / 8
4
4
7
8
Female / 4
1
1
2
2 / 3
1
2
3
1
Perform the appropriate statistical test for this data set to determine how gender and repair-type affect the time it takes to make a repair (use alpha=.05). Produce a plot of this data, and paste below the appropriate table and plot:
Based on this information, who would you assign to each type of repair for the next NASA mission (remember, you must assign one female and one male)?
9. / A social psychologist believes that people drink more alcohol when they are in a bad mood. However, he has also noticed that underlying depression also affects how much alcohol people consume. He recruits 16 participants (8 of them are depressed, and the other 8 are not depressed) into his experimental study, in which he makes half of the depressed group and half of the non-depressed group happy by showing them pictures of babies, puppies, and kittens. The other half of each group is shown sad photos of people crying and war footage. He then allows each person to consume as much alcohol as they please, recording how many servings they have consumed. Test the hypothesis that mood and depression affect alcohol consumption (use alpha=.05).
Depressed / Not Depressed
Happy / 2
3
1
6 / 11
9
7
12
Sad / 9
9
12
9 / 4
5
1
2
- Report which main effects and or interaction effects are significant.
- Explain the pattern in the data. Who drinks more and under what conditions?
10. / The average household in America changes light bulbs about 5 times a year. General Electrics is unveiling a new light bulb which they claim will last longer than the average light bulb, and so it will have to be replaced less frequently. A research lab buys enough of these new light bulbs to fit 10 American households. After one year of use, they ask those families to report how many times they changed their bulbs. Below is the data. Test the hypothesis that these new bulbs last longer than the average light bulb.
x = {1, 1, 5, 1, 8, 1, 1, 2, 1, 9}
- What is the appropriate test?
- State the null hypothesis:
- State the alternative hypothesis:
- Find the critical value:
- Calculate the obtained statistic:
- Make a decision
- What does your decision mean?