# Applied Sciences

College of Doctoral Studies

**RES-845: Module 4 Problem Set**

**Problem 1:**

You have information on one sample and want to compare it to the population to see if it is significantly different from the population mean. In each of the following situations, would it be appropriate to use the t-test OR the z-test?

a. You know the population mean and variance

b. You do not know the population mean and variance

**Problem 2:**

Unlike the z-test that uses information about the population’s variance or SD, the formula for the t-statistic uses an *estimate of the population’s variance or standard deviation*, which is called the ______________________________ which is computed from the ____________________.

**Problem 3:**

a. A researcher wants to compare typing speed (the DV) in two conditions of light (IV: low, high level of light). In order to use a t-test for independent samples, the design had to have participants that were __________________________________________________.

b. To perform a t-test where we are comparing **two independent samples** (groups), we need three pieces of information. These are:

________________________________________________________

________________________________________________________

________________________________________________________

**Problem 4:**

The degrees of freedom (df) for each sample that is being compared using the t-test is computed as __________.

**Problem 5:**

When we did the z-test, we computed the z-value and then looked at where it would fall in the distribution of all possible z-scores. Similarly, when we do a t-test, we compute the t-value and then look at where that t-value would fall in the distribution of _______________________________________. The critical values of *t* can be found in Table ___ in the appendix of the textbook.

**Problem 6:**

a. A nondirectional hypothesis predicts there will be a significant difference between the two means that can be ___________________________________ . A directional hypothesis predicts there will be a significant difference between the two means and adds _____________________________.

b. A nondirectional hypothesis uses a ___-tailed test, while a directional hypothesis uses a ___-tailed test to evaluate if the difference between the means is significant.

c. When I set alpha at 5%, and have a ** nondirectional hypothesis **, the 5% of outcomes that occur less frequently than my critical t-value

1. Fall in one tail of the distribution OR

2. are divided between the two tails (2 ½% in one tail and 2 ½ % in the other tail)?

**Problem 7:**

Go to Table B.2 in the appendix of your textbook, and decide whether the following t-value that has been computed is significant (that is, its value is equal to or greater than the t-value beyond which only 5% or less of the proportion of all possible t-values would occur), given the df, the type of hypothesis (directional/nondirectional), the alpha level, the required (critical) t-value, and the actual t-value that was computed to compare the means of Group A with Group B.

a. Hypothesis: There will be a significant difference between the means of Group A and Group B; df = 25; computed t-value = 2.35.

1. Is this a directional or nondirectional hypothesis?____________

2. Given the type of hypothesis, the proportion of extreme values that I am interested in will be found in one tail or in two tails combined?

3. Given that the df = 25 and alpha is .05, what would be the value of t that my computed value would have to equal or exceed?

4. Is my computed value significant at this alpha level?

Answers to a:

b. Hypothesis: There will be a significant difference between the means of Group A and Group B; specifically, the mean of Group B will be significantly greater than the mean of Group A; df = 25; computed t-value = 2.35.

5. Is this a directional or nondirectional hypothesis?____________

6. Given the type of hypothesis, the proportion of extreme values that I am interested in will be found in one tail or in two tails combined?

7. Given that the df = 25 and alpha is .05, what would be the value of t that my computed value would have to equal or exceed?

8. Is my computed value significant at this alpha level?

**Problem 8:**

Research has shown that people are more likely to show dishonest and self-interested behaviors in darkness than in a well-lit environment (Zhong, Bohns, & Gino, 2010). In one experiment, participants were given a set of 20 puzzles and were paid $0.50 for each one solved in a 5-minute period. However, the participants reported their own performance and there was no obvious method for checking their honesty. Thus, the task provided a clear opportunity to cheat and receive undeserved money. One group of participants was tested in a room with dimmed lighting and a second group was tested in a well-lit room. The reported number of solved puzzles was recorded for each individual. The following data represent results similar to those obtained in the study.

Group A
Well-Lit Room |
Group B
Dimly Lit Room (Is there a treatment effect of lighting?) |

7 | 9 |

8 | 11 |

10 | 13 |

6 | 10 |

8 | 11 |

5 | 9 |

7 | 15 |

12 | 14 |

5 | 10 |

a. Is there a significant difference in reported performance between the two conditions? Use two-tailed test with alpha set at p < .01.

b. Compute Cohen’s *d *to estimate the size of the treatment effect. After you have computed Cohen’s *d*, how would you interpret it?

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