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# State the null and alternative hypotheses both in words and in symbols define all the symbols you use

INSTRUCTIONS TO CANDIDATES

### Assignment

Note: You will turn in your work independently on this assignment. Conduct all the analyses by SPSS and cut and paste only the relevant outputs adjacent to the texts.

This is a “pick two” so pick two of the following three questions to answer.

1. The amount of money spent on health care is an important issue for workers because many companies provide health insurance that only partially covers many medical procedures. The director of employee benefits at a midsize company wants to determine the amount spent on health care by the typical hourly worker in the company and she wants to know whether the typical worker spend more than \$350 per year on health care needs. A random sample of 25 workers is selected.  The amount they spend on their families’ health care needs during the past year is given here and also provided as a SPSS data set: “Health care cost.sav”.

400, 345, 248, 590, 398, 418, 197, 342, 328, 397, 531, 172, 521, 431, 254, 495, 642, 219, 276, 326, 354, 225, 183, 365, 428

(a)    State the null and alternative hypotheses both in words and in symbols. Define all the symbols you use (see how I do this in the slides when I show you a formula and then use a “where” followed by description of each).

(b)   Discuss which test is appropriate in terms of (i) type of test, i.e., z-test or t-test; (ii) type of method, i.e., (a) one-sample, (b) two paired (related) samples, or (c) two independent samples; and (iii) directionality of the test, i.e., one-tailed or two-tailed test. Give the reasons of your choice for each aspect.

(c)    Conduct the appropriate analysis by SPSS. That is, test the hypothesis at a = .05 level.

(d)   Check the assumptions that are made for this test.

a. Normality (create histogram of this sample and think about the shape of the distribution)

b. Independent observations (think about the role of random selection)

(e)    Make a statistical decision and write a short substantive interpretation of the results of the test. Be sure to include the value of the effect size (i.e., Cohen’s d) and comment on that.

2.   Hout, Duncan, and Sobel (1987) reported on the relative sexual satisfaction of married couples. They asked each member of 91 married couples to rate the degree to which they agreed with “Sex is fun for me and my partner” on a four-point scale ranging from “never or occasionally” to “almost always.” They wanted to know whether couples’ sexual satisfaction levels are comparable. The data appear below and also are in Couples sexual satisfaction.sav.

 Husband 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Wife 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 Husband 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 Wife 3 4 4 4 1 1 2 2 2 2 2 2 2 2 3 Husband 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 Wife 3 3 4 4 4 4 4 4 4 1 2 2 2 2 2 Husband 3 3 3 3 3 3 3 3 3 3 3 3 1 4 4 Wife 3 3 3 3 4 4 4 4 4 4 4 4 4 1 1 Husband 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Wife 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 Husband 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Wife 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 Husband 4 Wife 4

(a)    State the null and alternative hypotheses both in words and in symbols. Define all the symbols you used.

(b)   Discuss which test is appropriate in terms of (i) type of test, i.e., z-test or t-test, (ii) type of method, i.e., (a) one-sample, (b) two paired (related) samples, or (c) two independent samples, and (iii) directionality of the test, i.e., one-tailed or two-tailed test. Give the reasons of your choice for each aspect.

(c)    Conduct the appropriate analysis by SPSS. That is, test the hypothesis at a = .05 level.

(d)   Check the assumptions that are made for this test.

a. normality (think about two things: sample size and distribution of the differences)

b. independent observations (hmmm…husbands and wives probably talk, so something else)

(e)    Make a statistical decision and write a short substantive interpretation of the results of the test. Be sure to include the value of the effect size (i.e., Cohen’s d) and comment on that.

3. The Thematic Apperception Test (TAT) presents subjects with ambiguous pictures and asks then to tell a story about them. These stories can be scored in any number of ways. Werner, Stabenau, and Pollin (1970) asked mothers of 20 Normal and 20 Schizophrenic children to complete TAT and scored for the number of stories (out of 10) that exhibited a positive parent-child relationship. They wanted to know whether the mean TAT score for schizophrenic children is lower than that for normal children. The data are in the following table are also in the TAT.sav:

 Normal 8 4 6 3 1 4 4 6 4 2 Schizophrenic 2 1 1 3 2 7 2 1 3 1 Normal 2 1 1 4 3 3 2 6 3 4 Schizophrenic 0 2 4 2 3 3 0 1 2 2

(a)    State the null and alternative hypotheses both in words and in symbols. Define all the symbols you used.

(b)   Discuss which test is appropriate in terms of (i) type of test, i.e., z-test or t-test, (ii) type of method, i.e., (a) one-sample, (b) two paired (related) samples, or (c) two independent samples, and (iii) directionality of the test, i.e., one-tailed or two-tailed test. Give the reasons of your choice for each aspect.

(c)    Conduct the appropriate analysis by SPSS. That is, test the hypothesis at a = .05 level.

(d)   Check the assumptions that are made for this test.

a. normality

b. homogeneity of variance (hint: Levene’s test)

c. independence

(e)    Make a statistical decision and write a short substantive interpretation of the results of the test. Be sure to include the value of the effect size (i.e., Cohen’s d) and comment on that.

(f)    BONUS QUESTION: In this problem, a significant difference might lead someone to suggest that poor parent-child relationships are the cause of schizophrenia. What might this be a troublesome conclusion? Discuss it from perspectives of research design and internal validity.

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