Statistics -Topic 7 & One project

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PSY520 – Module 7

Answer Sheet

Submit your answers in the boxes provided. No credit will be given for responses not found in the correct answer area.

Chapter 19:

19.9 Randomly selected records of 140 convicted criminals reveal that their crimes were committed on the following days of the week:

DAYS WHEN CRIMES WERE COMMITTED
FREQUENCY	MON.	TUE.	WED.	THU.	FRI.	SAT.	SUN.	TOTAL
Observed (ƒₒ)	17	21	22	18	23	24	15	140

Question:	Calculations or Logic:	Answer:
Using the .01 level of significance, test the null hypothesis that in the underlying population, crimes are equally likely to be committed on any day of the week.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What are the degrees of freedom?
		What is the decision rule?
	Step 4	What is the critical X2?
		What is the value of X2? (you will need to calculate this)
	Step 5	What is the decision? (retain or reject the null hypothesis at the specified level of significance; note the relationship between the observed and critical X2 scores)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Specify the p -value for this test result.
How might this result be reported in the literature?

19.10 While playing a coin-tossing game in which you are to guess whether heads or tails will appear, you observe 30 heads in a string of 50 coin tosses.

Question:	Calculations or Logic:	Answer:
Test the null hypothesis that this coin is unbiased, that is, that heads and tails are equally likely to appear in the long run.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What are the degrees of freedom?
		What is the decision rule?
	Step 4	What is the critical X2?
		What is the value of X2? (you will need to calculate this)
	Step 5	What is the decision? (retain or reject the null hypothesis at the specified level of significance; note the relationship between the observed and critical X2 scores)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Specify the p -value for this test result.

19.13 In 1912, over 800 passengers perished after the ocean liner Titanic collided with an iceberg and sank. The table below compares the survival frequencies of cabin and steerage passengers.

ACCOMMODATIONS ON THE TITANIC
SURVIVED	CABIN	STEERAGE	TOTAL
YES	299	186	485
NO	280	526	806
TOTAL	579	712	1291

Source: MacG. Dawson, R .J. (1995). The “unusual” episode data revisited. Journal of Statistical Education, 3, no. 3.

Question:	Calculations or Logic:	Answer:
Using the .05 level of significance, test the null hypothesis that survival rates are independent of the passengers’ accommodations (cabin or steerage).	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What are the degrees of freedom?
		What is the decision rule?
	Step 4	What is the critical X2?
		What is the value of X2? (you will need to calculate this)
	Step 5	What is the decision? (retain or reject the null hypothesis at the specified level of significance; note the relationship between the observed and critical X2 scores)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Assuming a significant x², estimate the strength of the relationship.
What is the strength of this relationship? (small, medium, large or very large)?
To more fully appreciate the importance of this relationship, calculate an odds ratio to determine how much more likely a cabin passenger is to have survived than a steerage passenger.

19.14 In a classic study, Milgram et al. “lost” stamped envelopes with fictitious addresses (Medical Research Association, Personal Address, Friends of Communist Party, and Friends of Nazi Party).* One hundred letters with each address were distributed among four locations (shops, cars, streets, and phone booths) in New Haven Connecticut, with the following results:

ADDRESS	RETURNED	NOT RETURNED	TOTAL
Medical Research Association	72	28	100
Personal Address	71	29	100
Friends of Communist Party	25	75	100
Friends of Nazi Party	25	75	100
Total	193	207	400

*Milgram, S., Mann, L., & Harter, L. (1965). The Lost Letter Technique: A Tool of

Social Research. Public Opinion Quarterly, 29, 437–438.

Question:	Calculations or Logic:	Answer:
Using the .05 level of significance, test the null hypothesis that address does not matter in the underlying population.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What are the degrees of freedom?
		What is the decision rule?
	Step 4	What is the critical X2?
		What is the value of X2? (you will need to calculate this)
	Step 5	What is the decision? (retain or reject the null hypothesis at the specified level of significance; note the relationship between the observed and critical X2 scores)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Specify the approximate p -value for this result.
Assuming a significant x², estimate the strength of the relationship.
What is the strength of this relationship? (small, medium, large or very large)?
How might these results be reported in the literature?
Collapse the original 4 x 2 table to a 2 x 2 table by combining the results for the two neutral addresses and for the two inflammatory addresses. Calculate the odds ratio for returned letters.

19.16 A social scientist cross-classifies the responses of 100 randomly selected people on the basis of gender and whether or not they favor strong gun control laws to obtain the following:

GENDER AND ATTITUDE TOWARD STRONG GUN CONTROL
ATTITUDE TOWARD GUN CONTROL
GENDER	FAVOR	OPPOSE	TOTAL
MALE	40	20	60
FEMALE	30	10	40
TOTAL	70	30	100

Question:	Calculations or Logic:	Answer:
Using the .05 level of significance, test the null hypothesis for gender and attitude toward gun control.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What are the degrees of freedom?
		What is the decision rule?
	Step 4	What is the critical X2?
		What is the value of X2? (you will need to calculate this)
	Step 5	What is the decision? (retain or reject the null hypothesis at the specified level of significance; note the relationship between the observed and critical X2 scores)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Specify the approximate p -value for this result.
How might these results be reported in the literature?

Chapter 20:

20.5 A group of high-risk automobile drivers (with three moving violations in one year) are required, according to random assignment, either to attend a traffic school or to perform supervised volunteer work. During the subsequent five-year period, these same drivers were cited for the following number of moving violations:

NUMBER OF MOVING VIOLATIONS

TRAFFIC SCHOOL

VOLUNTEER WORK

Question:	Calculations or Logic:	Answer:
Why might the Mann-Whitney U test be preferred to the t test for these data?
Use U to test the null hypothesis at the .05 level of significance.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What is the sample size?	Group 1:
			Group 2:
		What is the sum of ranks?	Group 1:
			Group 2:
		What is the decision rule?
	Step 4	What is the critical U?
		What is the value of U? (you will need to calculate this)	U1:
			U2:
			U:
	Step 5	What is the decision? (retain or reject the null hypothesis)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Specify the approximate p -value for this result.

20.6 A social psychologist wishes to test the assertion that our attitude toward other people tends to reflect our perception of their attitude toward us. A randomly selected member of each of 12 couples who live together is told (in private) that his or her partner has rated that person at the high end of a 0 to 100 scale of trustworthiness. The other member is told (also in private) that this or her partner has rated that person at the low end of the trustworthiness scale. Each person is then asked to estimate, in turn, the trustworthiness of his or her partner, yielding the following results. (According to the original assertion, the people in the trustworthy condition should give higher ratings than should their partners in the untrustworthy condition.)

TRUSTWORTHINESS RATINGS
COUPLE	TRUSTWORTHY (1)	UNTRUSTWORTHY (2)
A	75	60
B	35	30
C	50	55
D	93	20
E	74	12
F	47	34
G	95	22
H	63	63
I	44	43
J	88	79
K	56	33
L	86	72

Question:	Calculations or Logic:	Answer:
Use T to test the null hypothesis at the .01 level.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What is n?
		What is the decision rule?
	Step 4	What is the critical T?
		What is the value of T? (you will need to calculate this)	R+:
			R-:
			T:
	Step 5	What is the decision? (retain or reject the null hypothesis)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Specify the approximate p -value for this result.

20.7 Does background music influence the scores of college students on a reading comprehension test? Sets of 10 randomly selected students take a reading comprehension test with rock, country, or classical music in the background. The results are as follows (higher scores reflect better comprehension):

READING COMPREHENSION SCORES
ROCK (1)	COUNTRY (2)	CLASSICAL (3)
90	99	52
11	94	75
82	95	91
67	23	94
98	72	97
93	81	31
73	79	83
90	28	85
87	94	100
84	77	69

Question:	Calculations or Logic:	Answer:
Why might the H test be preferred to the F test for these data?
Use H to test the null hypothesis at the .05 level of significance.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What are the degrees of freedom?
		What is the decision rule?
	Step 4	What is the critical H?
		What is the value of H? (you will need to calculate this)
	Step 5	What is the decision? (retain or reject the null hypothesis)
	Step 6	What is your interpretation of the decision in relation to the original research problem?
Specify the approximate p -value for this result.

20.10 Use H rather than F to test the weight change data recorded in Review Question 16.13 on page 381.

Question:	Calculations or Logic:	Answer:
Use H rather than F to test the weight change data.	Step 1	What is the research problem?
	Step 2	What is the null hypothesis?
		What is the alternative hypothesis?
	Step 3	What are the degrees of freedom?
		What is the decision rule?
	Step 4	What is the critical H?
		What is the value of H? (you will need to calculate this)
	Step 5	What is the decision? (retain or reject the null hypothesis)
	Step 6	What is your interpretation of the decision in relation to the original research problem?