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ProblemSet 3.3: z Test
· Criterion: Calculate a z test to make a decision about a sample.
· Data: The average (mean) height for adult women is 65 inches, and the standard deviation is 3.5 inches. Given the women you know, you think this number is low; so, you record the heights of 25 of your female friends. The average height of your 25 friends is 66.84 inches.
Portion of the Normal Curve Table
|
z |
Area |
|||||||
|
1.92 |
.9726 |
2.27 |
.9884 |
2.62 |
.9956 |
2.97 |
.9985 |
|
|
1.93 |
.9732 |
2.28 |
.9887 |
2.63 |
.9957 |
2.98 |
.9986 |
|
|
1.94 |
.9738 |
2.29 |
.9890 |
2.64 |
.9959 |
2.99 |
· Instruction: Answer this: If your friends are just a representative sample of adult females, what is the probability that your friends are so tall?
(Assessment continues on next page.)
Problem Set 3.4: Independent Variables (IVs) and Dependent Variables (DVs)
· Criterion: Differentiate between independent and dependent variables.
· Data: A researcher randomly assigns a group of adults to one of two diets plans (Diet Plan A or Diet Plan B), and she then measures the amount of weight loss each experiences in a two-week period.
· Instruction: Answer the following:
· What is the IV in this study?
· What is the DV in this study?
Problem Set 3.5: Hypotheses
· Criterion: Write a directional-alternative hypothesis, nondirectional-alternative hypothesis, and null hypothesis.
· Data: A researcher is studying whether the amount of weight loss differs in participants who follow Diet Plan A versus those who follow Diet Plan B.
· Instruction: Write the following:
a. A directional alternative hypothesis.
b. A nondirectional alternative hypothesis.
c. The null hypothesis.
Problem Set 3.6: Errors and Significance: Type 1 and Type 2 Error
· Criterion: Differentiate between Type 1 and Type 2 error.
· Data: It is an established fact that in the general population, men weigh more on average than women. In a study, you randomly sample 100 men and 100 women, you record each participant’s weight, and you find that there is no significant difference in weight based on gender.
· Instruction: Answer the following:
· Given that a difference really does exist in the population, what type of error is this (Type 1 or Type 2)? Explain your answer.
Problem Set 3.7: Errors and Significance: Type 1 and Type 2 Error
· Criterion: Differentiate between Type 1 and Type 2 error.
· Data: In general, men and women do not differ on IQ. However, as part of your study, you found that women scored significantly higher than men on IQ.
· Instruction: Answer the following:
· Given that you found a difference in your study where none exists in the general population, identify the error (Type 1 or Type 2) and explain your answer.
(Assessment continues on next page.)
Problem Set 3.8: Hypothesis Testing and the z Score.
· Criterion: Evaluate a null hypothesis based on analysis of data.
· Data: Joan is 72 inches tall. The average (mean) height for adult women is 65 inches, and the standard deviation is 3.5 inches.
· Instructions:
a. State the null hypothesis.
b. State the alternative hypothesis.
c. Answer this: Joan is taller than what percentage of women in the population? (Hint: Think z score and area under the normal curve.)
d. Answer this: Given Joan’s height as compared to the population mean, do you expect to reject the null hypothesis? Explain your answer.
Problem Set 3.9: One-Sample t Test
Criterion: Hand calculate a one-sample t test.
Data: Rex’s Flower Shop advertised fresh cut roses that last longer than other roses. The mean vase life for a rose is 8 days. The following is a sample of the number of vase life days for 9 bouquets of roses from Rex’s Flower Shop: 8, 6, 12, 11, 8, 9, 14, 15, 10.
Instruction: Complete the following:
a. State the nondirectional hypothesis.
b. State the critical t for α = .05 (two tails).
c. Calculate t. Show your work.
d. Answer: Is the vase life of Rex’s roses significantly different than the population mean? Explain.
