Homework 7
Chapter 10: 12, 14, 15
10.12 For each of the following studies, say whether you would use a ttest for dependent means or a t test for independent means.
a) A researcher measures the heights of 40 college students who are the first born in their families and compares the 15 who come from large families to the 25 who come from smaller families.
The two samples must be independent, so use a test of independent means.
b) A researcher tests performance on a math skills test of each of 250 individuals before and after they complete a oneday seminar on managing test anxiety.
Same people tested twice (“before and after”), so use a dependent samples test
c) A researcher compares the resting heart rate of 15 individuals who have been taking a particular drug to the resting heart rate of 48 other individuals who have not been taking this drug.
The two samples must be independent, so use a test of independent means.
10.14 For each of the following experiments, decide if the difference between conditions is statistically significant at the 0.05 level (twotailed).








a.

10

604

60

10

607

50

b.

40

604

60

40

607

50

c.

10

604

20

40

607

16

a)
0.90 is not in the critical region (df= n_{1 }+ n_{2} – 2 = 18; t_{crit} = ±2.101), so we fail to reject the H_{0}
b)
1.81 is not in the critical region (df= n_{1 }+ n_{2} – 2 = 78; t_{crit} = ±2.0), so we fail to reject the H_{0}
c)
1.81 is not in the critical region (df= n_{1 }+ n_{2} – 2 = 18; t_{crit} = ±2.101), so we fail to reject the H_{0}

A psychologist theorized that people can hear better when the have just eaten a large meal. Six individuals were randomly assigned to eat either a large meal or a small meal. After eating the meal, their hearing was tested. The hearing ability scores (high numbers indicate greater ability) are given below. Using the 0.05 level, do the results support the psychologist’s theory?

Big Meal Group

Small Meal Group

Subject

Hearing

Subject

Hearing

A

22

D

19

B

25

E

23

C

25

F

21

mean

24


21

SS

6


8


Use the steps of hypothesis testing
H0: Hearing will be no different (or worse) for the group that ate a large meal ()
HA: Hearing will be better for the group that ate a large meal ()
1.81 is not in the critical region (df= n_{1 }+ n_{2} – 2 = 4; t_{crit} = 2.132), so we fail to reject the H_{0}
Conclude that the evidence does not support the claim that hearing is affected by meal size

Sketch the distributions involved

Explain your answers to someone who has never had a course in statistics
Answers will vary, should be something about how the observed difference between the groups is not above and beyond what you might expect based on random chance
Additional SPSS problems
Download the following file: height.sav
1) Using SPSS, compute the correlation matrix which includes the following variables:
◦ average parents height
◦ income
◦ average calcium intake
◦ age
◦ weight
◦ height
Print out the correlation matrix and include it in your homework answers (or write it out).
Which of the correlations are statistically significant? Write out a description of each of these significant correlations.
Avg height of parents is significantly positively correlated with calcium intake (.52), weight (.66), and height (.80)
Household income is significantly positively correlated with age (.33)
Avg calcium intake is significantly positively correlated with height (.41)
Weight is significantly positively correlated with height (.79)
2) Compare a two regression models predicting height.
◦ Model 1: average parents height & calcium intake
◦ Model 2: average parents height, calcium intake, income, & weight
Describe each model (rsquared & whether the explanatory variables within each model are statistically significant). Also compute the change rsquared going from model 1 to model 2. Is this change statistically significant? What does this result suggest to you about selecting between model 1 and model 2?

Model 1: average parents height & calcium intake

r^{2} = 0.641


Variables

Standardized betas

t

p

avg parent height

0.81

6.98

<0.001

Avg calcium intake

0.01

0.07

0.941

These results suggest that Model 1 accounts for 64.1% of the variance in height, and that average parent height is the only variable that accounts for a significant amount of this variance (calcium intake doesn’t account for a significant amount of it)

Model 2: average parents height, calcium intake, income, & weight

r^{2} = 0.75


Variables

Standardized betas

t

p

avg parent height

0.456

3.77

<0.001

Avg calcium intake

0.028

0.30

0.765

Household income

0.087

1.07

0.294

Weight

0.475

4.44

<0.001

These results suggest that Model 2 accounts for 75% of the variance in height, and that average parent height and weigth are the only variables that account for a significant amount of this variance.
The change r^{2} statistic [F(2,35)=10.48, p < 0.001] suggests that the change in variance accounted for from Model 1 to Model 2 is statistically significant. So we may conclude that model 2 does a better job predicting height. 