# Before you record or analyze the data, can you assume that the sampling distribution of the mean for this test will be normally distributed?

Problem Set 5.1: Central Limit Theorem

Criterion: Determine if a distribution will be normally distributed based on sample size.
Data: As part of a large research study, you administer a new test to 20,000 adults.
Instruction: Answer the following:

o Before you record or analyze the data, can you assume that the sampling distribution of the mean for this test will be normally distributed?

o Why or why not?
Problem Set 5.2: Standard Error of the Mean

Criterion: Calculate the standard error of the mean.
Data: College students in a large psychology class take a final exam. The mean exam score is 85, and the standard deviation is 5.

Instruction: Using the formula for σM, what will the standard error of the mean (σM ) be when:

a. the sample size is 25.

b. the sample size is 16.

c. the sample size is 20.
Problem Set 5.3: Calculate 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

(Assignment continues on next page.)

Instruction: Answer this question: If your friends are just a representative sample of adult females, what is the probability that your friends are so tall?

Problem Set 5.4: 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 adult 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 5.5: Hypotheses

Criterion: Write a directional alternative hypothesis, non-directional 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 5.6: 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 5.7: 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 in IQ. However, as part of your study, you found that women scored significantly higher than men in 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.

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Problem Set 5.8: Hypothesis Testing and the z Score.

Criterion: Evaluate a null hypothesis based on the 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.

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