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3. Time for some tedious, by-hand practice just to see if you can get the numbers right. Using the following information, calculate the t-test statistics by hand.

- X1 = 62 X2 = 60 n1 = 10 n2 = 10 s1 = 2.45 s2 = 3.16
- X1 = 158 X2 = 157.4 n1 = 22 n2 = 26 s1 = 2.06 s2 = 2.59
- X1 = 200 X2 = 198 n1 = 17 n2 = 17 s1 = 2.45 s2 = 2.35

4. Using the results you got from Question 3, and a level of significance of .05, what are the two-tailed critical values associated with each? Would the null hypothesis be rejected?

5. Here's a good one to think about. A public health researcher tested the hypothesis that providing new car buyers with child safety seats will also act as an incentive for parents to take other measures to protect their children (such as driving more safely, child-proofing the home, etc.). Dr. L counted all the occurrences of safe behaviors in the cars and homes of the parents who accepted the seats versus those who did not. The findings? A significant difference at the .013 level. Another researcher did exactly the same study, and for our purposes, let's assume that everything was the same—same type of sample, same outcome measures, same car seats, and so on. Dr. R's results were marginally significant (remember that from Chapter 9?) at the .051 level. Whose results do you trust more and why?

7. **One Sample T Test Practice with SPSS**

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

- State the RESEARCH Hypothesis or H1
**The students at our school score differently on a grammar test than the national population of readers.**

- State the NULL Hypothesis or Ho
**H0: There is no difference in the scores of students at our school and the national population of readers**

- Identify H1 as one or two-tailed
**This is a two-tailed test**

- Specify alpha level (level of significance)
- Alpha level = .05

- Specify Degrees of Freedom (n - 1)
**Degrees of freedom = 9 (note that SPSS will also give you this)**

- Identify Critical Value—(t
_{crit}) from the t table (in the appendix)**Critical value = +/- 2.262**

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

One-Sample Statistics | ||||||||
---|---|---|---|---|---|---|---|---|

N | Mean | Std. Deviation | Std. Error Mean | |||||

Grammar | 10 | 77.70 | 11.461 | 3.624 | ||||

One-Sample Test | ||||||||

Test Value = 89 | ||||||||

t | df | Sig. (2-tailed) | Mean Difference | 95% Confidence Interval of the Difference | ||||

Lower | Upper | |||||||

Grammar | -3.118 | 9 | .012 | -11.300 | -19.50 | -3.10 | ||

- State decision (rejection) rule -use the diagram of the normal distribution curve
- If the calculated t is beyond the t crit, then the NULL is rejected
- 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.**

- 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.

8. The population mean m 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.

- State the RESEARCH Hypothesis or H1
- State the NULL Hypothesis or Ho
- Identify H1 as one or two-tailed
- Specify alpha level (level of significance)
- Specify Degrees of Freedom (n - 1)
- Identify Critical Value—(t
_{crit}) from the t table (in the appendix) - Calculate t-score—(
_{tobt}) using SPSS (this has been done for you and the following printout shows the analysis of the data. - State decision (rejection) rule -use the diagram of the normal distribution curve
- If the calculated t is beyond the t crit, then the NULL is rejected
- If the calculated t not beyond the cril, then there is a FAILURE to reject the NULL
- State the meaning of the results, explain the outcome, and draw a conclusion.

**9. Independent** **Samples T test Practice with SPSS**

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:

No course | Course |

11 | 13 |

14 | 16 |

10 | 14 |

12 | 17 |

8 | 11 |

15 | 14 |

12 | 15 |

13 | 18 |

9 | 12 |

11 | 11 |

- What are the independent and dependent variables?
- State the null and alternative hypotheses.
- Using an alpha = 0.05, what is t (
_{crit})? - Using SPSS, calculate t (
_{obt}) - What should you conclude?

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