HYPOTHESIS TESTING EXERCISE
The following exercise is designed to help you understand the nature of hypothesis testing. For each of the questions outlined below, state the null hypothesis, the alternative and interpret the results to indicate if you reject, or fail to reject, the null. For each question below, consider the following question:
What does this mean in terms of the alternative hypothesis?
Note that it may be helpful to broaden your horizons and look into other textbook chapters than we have already covered or external resources (e.g. texts, internet, etc).
Situation: Jack and Jill are walking up the hill to fetch a pail of water.
1. Jack has noticed that as they walk up the hill, the air seems to be getting thinner. He collects air samples and measures these, he believes he will find a correlation between altitude and air density:
Null:
Alternative:
Finding: Correlation: .345 p < .001
Does this support the alternative hypothesis and what does this mean?
2. Jack said that men are faster at walking up the hill because they are stronger. Jill said that women would be because females have higher endurance. They collected a sample of men and women and measured their walking speed up the hill. The results are:
What is the dependent variable:
What is the categorical variable: At how many levels:
What is the appropriate test:
Null:
Alternative:
INDEPENDENT SAMPLES T-TEST ON SPEED GROUPED BY SEX
GROUP N MEAN SD
(women) 2.000 24 4.164 1.260
(men) 1.000 21 5.227 1.045
(P Value)
SEPARATE VARIANCES T = -2.613 DF = 23.3 PROB = 0.015
POOLED VARIANCES T = -2.435 DF = 33 PROB = 0.020
Does this support the alternative hypothesis and what does this mean?
3) Jill said that she thinks that left-handed men will be more likely to fall down at the top of the hill than women. Jack thinks that this is not true. They set up an experiment to test this. This is a 2x2 factorial design as follows:
|
|
Rt. Hand
|
Left Hand
|
|
Men
|
1: 3.5
|
2: 5.2
|
|
Women
|
3: 3.8
|
4: 4.2
|
What is the dependent variable:
What are the categorical variables: At how many levels:
What is the appropriate test:
Null:
Alternative:
ANALYSIS OF VARIANCE
SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P Value
SEX 8.525 1 8.525 5.928 0.020
ERROR 47.455 33 1.438
TUKEY HSD MULTIPLE COMPARISONS.
MATRIX OF PAIRWISE COMPARISON PROBABILITIES:
1 2 3 4
1 1.000
2 0.021 1.000
3 0.359 0.023 1.000
4 0.054 0.001 0.062 1.000
Does this support the alternative hypothesis and what does this mean?
Chart the results.