# Statistics Questions

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.

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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.

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.

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.

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.

(Assignment continues on next page.)
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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