Statistic SPSS

One Sample T Test Practice with SPSS

1. We want to test if students at our school score differently on a grammar test than the national population of readers (where μ = 89). We take a sample of ten (n=10) readers whose grammar reading scores are given below. Use this as a sample to do the other questions below.

72 67 59 76 93 90 75 81 71 93

1. State the RESEARCH Hypothesis or H1

a. The students at our school score differently on a grammar test than the national population of readers.

2. State the NULL Hypothesis or Ho

a. H0: There is no difference in the scores of students at our school and the national population of readers

3. Identify H1 as one or two-tailed

a. This is a two-tailed test

4. Specify alpha level (level of significance)

a. Alpha level = .05

5. Specify Degrees of Freedom (n – 1)

a. Degrees of freedom = 9 (note that SPSS will also give you this)

6. Identify Critical Value—(tcrit) from the t table (in the appendix)

a. Critical value = +/- 2.262

7. Calculate t-score—(tobt) using SPSS (this has been done for you and the results are given below: t obt= -3.118

8. State decision (rejection) rule –use the diagram of the normal distribution curve

a. If the calculated t is beyond the t crit, then the NULL is rejected

b. If the calculated t not beyond the crit, then there is a FAILURE to reject the NULL

If t obt is beyond 2.262 in the right tail or beyond -2.262 in the left tail, we have a rejection of the null hypothesis and we can accept the research hypothesis.

9. State the meaning of the results, explain the outcome, and draw a conclusion.

T obt is beyond t crit in the left tail; therefore, reject the null hypothesis; the reading scores of children in our school are lower than the scores of the national population. They are significantly lower.

Note: SPSS will always calculate significance on a two-tailed test. If you have a one-tailed test you will need to take t crit from the tables.

2. The population mean on a national scholastic achievement test is 100 with a standard deviation of 30. The students in Mr. Smart’s class got the following scores:

127 121 123 128 118 126 120 130 128 119 127 125

Using the criterion of 0.05 in the upper tail only, determine if Mr. Smart’s class is representative of the population.

1. State the RESEARCH Hypothesis or H1

2. State the NULL Hypothesis or Ho

3. Identify H1 as one or two-tailed

4. Specify alpha level (level of significance)

5. Specify Degrees of Freedom (n – 1)

6. Identify Critical Value—(tcrit) from the t table (in the appendix)

7. Calculate t-score—(tobt) using SPSS (this has been done for you and the following printout shows the analysis of the data.

8. State decision (rejection) rule –use the diagram of the normal distribution curve

a. If the calculated t is beyond the t crit, then the NULL is rejected

b. If the calculated t not beyond the cril, then there is a FAILURE to reject the NULL

9. State the meaning of the results, explain the outcome, and draw a conclusion.

3. On a national test of “mental intensity,” is 20 and the standard deviation 6.28. Students in your class produce the following scores:

25, 26, 34, 14, 33, 29, 22, 18, 16, 13, 21, 20, 22, 21, 34, 30

Using the criterion of 0.05 and both tails of the sampling distribution, determine if your class is representative of the population.

1. State the RESEARCH Hypothesis or H1

2. State the NULL Hypothesis or Ho

3. Identify H1 as one or two-tailed

4. Specify alpha level (level of significance)

5. Specify Degrees of Freedom (n – 1)

6. Identify Critical Value—(tcrit) from the t table (in the appendix)

7. Calculate t-score—(tobt) using SPSS(this has been done for you and the following printout shows the analysis of the data.

8. State decision (rejection) rule –use the diagram of the normal distribution curve

a. If the calculated t is beyond the t crit, then the NULL is rejected

b. If the calculated t not beyond the cril, then there is a FAILURE to reject the NULL

9. State the meaning of the results, explain the outcome, and draw a conclusion.

Paired Sample T test Practice with SPSS

1. We ask whether people will score higher or lower on a questionnaire of their well-being when they are exposed to sunshine compared to when they’re not exposed to sunshine. A sample of 8 people is first measured after low levels of sunshine exposure and then again after high levels of exposure. We get the following pairs of scores:

Low: 14 13 17 15 18 17 14 16

High: 18 12 20 19 22 19 19 16

a. What are the independent and dependent variables?

b. State the null and alternative hypotheses.

c. Using an alpha = 0.05, what is t (crit)?

d. Using SPSS, calculate t (obt)

e. What should you conclude?

2. Martha believes that a relaxation technique involving visualization will help people with mild insomnia fall asleep faster. She randomly selects 10 participants from a group of mild insomnia patients and measures how long (in minutes) it takes each one to fall asleep. Each participant is then taught the visualization technique and measured again to see how long it takes him or her to fall asleep. Her data are shown below.

a. What are the independent and dependent variables?

b. Using the fact that Martha believes the treatment will reduce the amount of time to fall asleep, state the null and alternative hypotheses.

c. Using an = 0.05, what is t crit?

d. Using SPSS, calculate t obt.

e. In plain English, what should Martha conclude?

Independent Sample T test Practice with SPSS

1. We investigate the effects of sensitivity training on a policeman’s effectiveness at resolving domestic disputes (comparing independent samples of policemen who had or had not completed the training). The dependent variable was their ability to successful resolve domestic disputes. The following scores were obtained:

a. What are the independent and dependent variables?

b. State the null and alternative hypotheses.

c. Using an alpha = 0.05, what is t (crit)?

d. Using SPSS, calculate t (obt)

e. What should you conclude?

2. Martha believes that a relaxation technique involving visualization will help people with mild insomnia fall asleep faster. She randomly selects a sample of 20 participants from a group of mild insomnia patients and randomly assigns 10 to receive visualization therapy. The other 10 participants receive no treatment. Each participant then is measured to see how long (in minutes) it takes him or her to fall asleep. Her data are shown below.

a. What are the independent and dependent variables?

b. Using the fact that Martha believes the treatment will reduce the amount of time to fall asleep, state the null and alternative hypotheses.

c. Using an alpha = 0.05, what is t (crit)?

d. Using SPSS, calculate t (obt)

e. What should you conclude?