Question

For each of the following scenarios, select the test (from the choices below), that is most appropriate for analyzing the data.

• a) Z-test

• b) One-sample t-test

• c) Independent t-test

• d) Dependent t-test

• e) 1-Way ANOVA

• f) Regression/Correlation

• g) Chi-Square

1. A psychologist wants to know if children with a schizophrenic parent are less well-adjusted than the general population, so she gives 20 children of schizophrenics a measure of psychological adjustment which has a mean of 35 in the general population.

2. A researcher wants to know if 5-yr-old boys and girls differ in their social skills. He recruits 30 brother and sister pairs and administers a social skills inventory with scores that can range from 0 to 80.

3. A sample of 60 children are asked to choose their favorite toy among 3 options (stuffed bear, stuffed dog, stuffed cat). Do children prefer these 3 toys equally?

4. Do married people who have had a greater number of sexual partners in the past report a greater desire to cheat on their spouse (desire to cheat measured on a 10-point scale)?

5. Among people who own pets, are women more likely than men to own cats rather than dogs?

6. Are people more likely to endorse positive rather than negative traits when describing themselves? Participants in a study are asked to rate (on a 7-point scale) the extent to which they possess various traits. Half of the traits they rate themselves on are positive traits and the other half are negative traits.

7. Does caffeine help test performance? 90 participants are randomly assigned to one of 4 groups (no caffeine, small dose, medium dose, and large dose) and then asked to complete a GRE math section.

8. Do seniors study for fewer hours per week than freshmen?

9. Is the average SAT math score of Hunter College students higher than the national average (μ = 500, σ = 100)?

10. Do students’ GPAs tend to improve from freshman to sophomore year?

11. Do more depressed students (depression measured on a 50-point scale) have lower GPAs?

Answer 1

1) Answer is

b) One sample t test

Note : We have sample mean of from a sample size 20 (small sample size ) , we have to compare it with population mean of general population , the null and alternative hypothesis is

We use one sample t test .

2) Answer is

d) dependent t test

Note : As sample is paired observations and we have to compare means , we use paired sample t test .

3) Answer is

g) Chi square

Note : We have to test whether the proportion of children are same who prefer each type , this is a test of multiple proportions, so we use chi square test of goodness of fit.

4) Answer is

f) Regression / correlation

Note : with the sample observation , we test whether there is relation between number of partners and greater desire to cheat, and also we can test whether the correlation is positive .

5) Answer is

g) Chi square

Note : We can do chi square test of independence to see preference of dogs or cats is independent of gender .

6) Answer is

a) z test

Note : We use z test for proportions

7) Answer is

e) one way ANOVA

Note : We compare mean score of GRE math of 4 groups

8) Answer is

c)  Independent t test

Note : We compare means of two indepndent samples , seniors and freshmen

9) answer is

a) z test

Note : We compare mean with national average , as population standard deviation is provided , we conduct one sample z test for mean

10) Answer is

d) dependent t test

Note : We collect paired observation(GPA) on same set of students for both year , and conduct paired t test .

11) Answer is

f) correlation/regression

Note : From sample observation we test that there is any positive correlation exists .