Posted: November 7th, 2022

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- 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.)*

- 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?

- 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.

- 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.

- 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.)*

- 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.

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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