1. Alpha (α) represents the area
a) In the tails of the distribution
b) Towards the center of the distribution
c) Higher than the mean of the distribution
d) Lower than the mean of the distribution
2. The independent sample t test, has a degrees of freedom equal to:
a) Number of observations in both samples plus 1
b) Number of observations in both samples
c) Number of observations in both samples minus 1
d) Number of observations in both samples minus 2
e) Number of observations in both samples minus three
3. The level of probability at which a null hypothesis can be rejected with confidence is known as the:
a) Level of significance
b) Distribution
c) Degrees of freedom
d) All of the above
4. If the sample standard deviation (s), sample size, and means are given, then employ a
a) T test
b) Z test
c) F test
5. If population standard deviation (σ), sample size, and means are given, then employ a
a) T test
b) Z test
c) Independent T test
d) F test
6. Suppose a computer software program such as SPSS performs an ANOVA and produces a p-value of 0.078. Should the null-hypothesis be rejected?
A. at α=0.01 level of significance?
a) Yes b) No
B. at α=0.05 level of significance?
a) Yes b) No
C. at α=0.10 level of significance?
a) Yes b) No
7. Determine what type of statistical test should be used to answer each of the questions below (You will only use each response one time).
a. One sample t -test
b. Dependent t -test
c. Iindependent t -test
d. Chi square (x2)
e. Anova
Suppose there is a city of 1 million residents with four neighborhoods: A, B, C, and D. A random sample of 650 residents of the city is taken and their occupation is recorded as "blue collar", "white collar", or "no collar".
What is the typical amount of money that a college student spends on clothes per year?
Are college students spending more this year than last year. One hundred people were asked at the end of last year how much money they have spent on clothing. The same people were then asked again at the end of this year.
Suppose you conducted a drug trial on a group of animals and you hypothesized that the animals receiving the drug would show increased heart rates compared to those that did not receive the drug
Student were given different drug treatments before revising for their 390LAB exam. Some were given a memory drug, some a placebo drug and some no treatment. The exam scores (%) were collected in a table for each group.
8. Place a T on the line if you think a statement it TRUE. Place an F on the line if you think the statement is FALSE
The objective of hypothesis testing is to prove whether or not the null hypothesis is correct.
Not all hypothesis testing involves two-tail tests.
It is easier to reject a null hypothesis using a 99% confidence level (α = 0.01) than a 95% confidence level (α = 0.05)
The only difference between the z and single sample t-test are the size of the samples.
The null hypothesis should be rejected when the p-value is larger than the significance level of the test.
A smaller p-value indicates more evidence that the null hypothesis isn't true
The correlation measures the strength and direction of the linear relationship between two quantitative variables.
The following plot displays a positive correlation:
9. The p- value for testing H0: µ=8 against H1: µ≠8 is 0.10. What decision can be made using a 0.05 significance level?
a) Reject H0 at 0.05
b) Fail to reject H0 at 0.05
c) Reject H1 at 0.05
d) Fail to reject H1 at 0.05
10. Imagine you've designed a method that you believe can teach algebra to people in a very short amount of time (15 minutes). To test this method, you recruit 10 random individuals and give them an algebra test of ten problems. You then have them work through your method for fifteen minutes and then they complete another algebra test of ten problems. Now you want to compare the scores on the pre and post-test to determine if scores improved after participants went through your training.
| Pretest number of correct answer |
Posttestnumber of correct answers |
| 6 |
7 |
| 5 |
5 |
| 4 |
7 |
| 3 |
5 |
| 5 |
5 |
| 6 |
5 |
| 6 |
5 |
| 8 |
9 |
| 3 |
6 |
| 5 |
3 |
| 2 |
5 |
a) Research question?
b) Hypothesis
c) Decision rule?
d) Results
t-score: ____ p-value: _____
Based on our degrees of freedom, what was our critical t? ____________
e) State your decision.
f) Interpretation of your results.
11. List the six steps of hypothesis testing
12. A study is testing methods to improve cognitive retention in Alzheimer's patients. Group A is the control group receiving no treatment, Group B is receiving the new method in training sessions and Group C is receiving the standard treatment. After the experiment is over and the data is collected you must determine whether the treatments are effective or not. Conduct a hypothesis test at α = 0.05
| No treatment Group A |
Treatment Group B |
Treatment Group C |
| 89 |
92 |
91 |
| 88 |
93 |
90 |
| 86 |
92 |
89 |
| 80 |
90 |
83 |
| 79 |
93 |
82 |
a) Research Question:
b) Decision Rule (dfb = k-1; dfw N-k)
F statistic=_________________ p-value = ____
c) Decision (reject or retain H0 at α = .05):
d) Interpretation:
Using Tukey post hoc analysis results, please report which group means vary significantly from which other group means:
13. In the following data a random sample was asked to rate their level of neighborliness as well as indicate their social class. At alpha level 0.05 test the null hypothesis that neighborliness does not vary by social class.
| Lower |
Working |
Middle |
Upper |
| 8 |
7 |
6 |
5 |
| 4 |
3 |
5 |
2 |
| 7 |
2 |
5 |
1 |
| 8 |
8 |
4 |
3 |
| 6 |
3 |
2 |
1 |
| 7 |
4 |
4 |
2 |
a) Research Question:
b) Decision Rule (dfb = k-1; dfw N-k)
F statistic=_________________ p=______
c) Decision (reject or retain H0 at α = .05):
d) Interpretation:
e) What two groups have significant differences (hint Tukey's) results?
14. Is there a linear relationship between the age at which a child first begins to speak and his or her mental ability later on? To answer this question a study was conducted in which the age (in months) at which a child first spoke and the child's score on an aptitude test as a teenager were recorded:
| Age |
Score |
| 15 |
95 |
| 26 |
71 |
| 10 |
83 |
| 9 |
91 |
| 15 |
102 |
| 20 |
87 |
| 18 |
93 |
| 11 |
100 |
| 8 |
104 |
| 20 |
94 |
a. Using your knowledge about correlation, using SPSS calculate the correlation (r) and describe the strength of the relationship.
r= _______
Description:
15. The following data refers to the horseback riding style (1=western; 2= English; 3 =bareback) and weekly riding time for 15 people with memberships at an equestrian center.
| Style |
Hours/week |
| 1 |
15 |
| 2 |
16 |
| 1 |
16 |
| 1 |
10 |
| 3 |
17 |
| 1 |
12 |
| 2 |
16 |
| 2 |
9 |
| 2 |
11 |
| 1 |
8 |
| 3 |
15 |
| 1 |
14 |
| 1 |
10 |
| 3 |
26 |
| 2 |
7 |
Input the data into SPSS and perform the appropriate ANOVA to compare the number of hours those who use each style of riding generally spend horseback riding during a week.
a. What is the value of F? __________ b. What is the value of p? __________
16.
a. What is your t-value? ____________
b. What is your p-value? ____________
c. Based on our degrees of freedom, what was our critical t? ____________
e. State your decision. Did you retain or reject the null hypothesis?
f. Interpret your results.
17. We will now review how to enter data and use SPSS to compare between the men's and women's 100m times in the 2006 Big West Championship Meet. Formulate a hypothesis and then enter the data into SPSS to run the test..
| Time in seconds |
Gender |
| 12 |
2 |
| 12 |
2 |
| 11 |
1 |
| 11 |
1 |
| 12 |
2 |
| 11 |
1 |
| 11 |
1 |
| 12 |
2 |
| 12 |
2 |
| 11 |
1 |
| 12 |
2 |
| 11 |
1 |
| 12 |
2 |
| 12 |
2 |
| 10 |
1 |
| 11 |
1 |
Identify the following:
a. t-score: ____________
b. 95% CI: ____________
c. Retain or Reject H0:___________
18. In the scatterplot below, the correlation is closest to
a. r = -0.87
b. r = 0.25
c. r = 0.99
d. r = 1.03
