simple maths

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.

· 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.