Complete the folloiwng:
Q1: 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?
Q2: 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:
o What is the IV in this study?
o What is the DV in this study?
Q3: 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.
Q4: 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:
o Given that a difference really does exist in the population, what type of error is this (Type 1 or Type 2)? Explain your answer.
Q5: 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:
o 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.)
Q6: 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.
Q7: 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.