# Sampling Methods and Hypothesis Testing

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10. A researcher wants to collect data about the study habits of sophomores at Harmond University. From the sophomore class of 2,300 students, she wants to collect a sample of 70 students.

Which of the following sampling methods will yield the most representative sample?

a. Assigning each sophomore a number and then randomly generating 70 numbers from that list.

b. Randomly selecting 70 sophomores entering the university's main library on a randomly selected evening.

c. Selecting the 70 sophomores whose grade point averages (GPA) fall closest to the mean GPA of the sophomore class.

d. Randomly selecting 70 sophomores who are members of college fraternities.

28. The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variables "US Gross Domestic Product (GDP) in trillions of dollars" and "average gas mileage of all passenger cars in miles per gallon (mpg)."

Which of the two independent variables is significant at the 0.01 level?

a. GDP only.

b. Average car gas mileage only.

c. Both independent variables.

d. Neither independent variable.

29. The regression analysis below relates US annual energy consumption in trillions of BTUs to the independent variables "US Gross Domestic Product (GDP) in trillions of dollars" and "average gas mileage of all passenger cars in miles per gallon (mpg)."

The coefficient for the independent variable "average car gas mileage (mpg)," -70.50, describes:

a. The relationship between energy consumption and average car gas mileage, controlling for GDP.

b. The relationship between energy consumption and average car gas mileage, not controlling for GDP.

c. The relationship between average car gas mileage and GDP, controlling for energy consumption.

d. The relationship between average car gas mileage and GDP, not controlling for energy consumption

30. The data table below tabulates a pizza parlor's advertising expenditures and sales for 8 consecutive quarters. The marketing manager wants to know how much of an impact current advertising will have on sales two quarters from now.

When running a regression with the dependent variable "sales" and the independent variable "advertising lagged by two quarters," how many data points can she use, given the available data?

a. 6

b. 7

c. 8

d. 9

https://brainmass.com/statistics/hypothesis-testing/sampling-methods-and-hypothesis-testing-524214

#### Solution Preview

10. A researcher wants to collect data about the study habits of sophomores at Harmond University. From the sophomore class of 2,300 students, she wants to collect a sample of 70 students.

Which of the following sampling methods will yield the most representative sample?

• Assigning each sophomore a number and then randomly generating 70 numbers from that list.

• Randomly selecting 70 sophomores entering the university's main library on a randomly selected evening.

• Selecting the 70 sophomores whose grade point averages (GPA) fall closest to the mean GPA of the sophomore class.

• Randomly selecting 70 sophomores who ...

#### Solution Summary

The solution responds to question 10, 28 and 29 only. The average car gas mileages are determined.

T tests, confidence intervals

1. Explain the difference between testing a single mean, testing the difference between two means from an "independent sample" and testing mean differences from a "dependent sample".

2. Choose a variable. You will be comparing the means of two groups to each other. Your sample will consist of 12 subjects in each group. You may collect data or create data.

a. Write a brief statement of purpose of the study

b. Define the two groups

c. State the hypotheses for the study

d. Select an alpha value

e. Show the raw data

f. Decide which statistical test is appropriate and compute the test statistic (independent samples t-test or dependent samples t-test). Why is the test appropriate?

g. Find the critical values(s)

h. State the decision

i. Summarize the results

3. What does increasing your level of confidence do to the interval estimate?

4. From your t distribution table and for df = 25, note whether the following t scores are significant at the alpha = .05 level for a one-tailed test; a two-tailed test.

a. t = -1.316

b. t = +.316

c. t = -2.660

d. t = 1.87

5. You are investigating the possible differences between males and females on the importance of communication. Your research hypothesis is that females place more importance on communication than males (higher scores indicate more importance). You have obtained the following data:

Male: sample size = 26, mean = 57.5, s = 9.7

Female: sample size = 24, mean = 65.0, s = 10.2

a. Is this a one-tailed or two-tailed test? Is this a dependent samples or independent samples t-test? What is your null hypothesis? What is your alternate hypothesis?

b. Perform the test at alpha = .05

c. Draw final conclusions