Posted: November 7th, 2022

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#### Problem Set 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

z

Area

z

Area

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

.9986

• 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.

• 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.

• 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.

• 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.

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