N6208 Assignment 5
Chapter 5 Hypothesis Testing
- Suppose you wanted to test the hypothesis that the average speed on a highway– where the maximum legal speed is 55 mph–is not equal to 55 mph (i.e., H0: μ = 55; H1: μ ≠ 55). Speed guns are used to measure the speed of 64 drivers, and the mean is found to be 57.2, SD = 8.0. What is the calculated value of t for a one-sample t-test? With α = .05 for a 2-tailed test, is the sample mean of 57.2 significantly different from the hypothesized mean of 55.0 (i.e., can the null hypothesis be rejected)?
Step 1: Specify the hypotheses (symbolically)
Null Hypothesis: _________________
Alternative hypothesis: ___________
α = 0.05 (two-tailed)
Step 2: Calculate the necessary statistics
SEM= 8.0 (SD) / 63 (n-1) = 0.127
√0.127= 0.356 (SD)
0.356 / √64
0.356 / 8 = 0.045
t = __________________
Step 3: Establish the critical value and region of rejection. (Drawing the picture helps you understand the process)
Step 4: Make a decision regarding the null hypothesis.
- The Polit2SetB contains standardized scores on the Short-Form Health Survey or SF12, a widely used 12-item health status measure. This scale yields two subscales scores: a physical health component subscale score (sf12phys) and a mental component subscale score (sf12ment). The data values for the women in this sample are standardized T scores that were created using national norms with a mean of 50.0 and an SD of 10.0. Because there are national norms, we can use a one sample t test to test the null hypothesis that the means for women in this sample on both subscales are 50.0.
To run a one-sample t test, click Analyze→ Compare Means→ One-sample T test. In the dialog box that appears, insert the two SF-12 variables, which are at the end of the file, in the Test Variable(s) slot. At the bottom, enter the Test Value as 50.0. Click the Options pushbutton to make sure that you are requesting 95% CIs for the analysis. Then click Continue→ OK to run the analysis and answer these questions:
a. Write a research question for the physical health component score.
b. State the null and alternative hypothesis (non-directional) for the physical health component score.
c. What are the values of t for the two analyses?
d. Are these values statistically significant? If so, at what level of significance?
e. Write a few sentences to summarize the results.
f. Include your spss printout to your assignment.
- How to increase power to decrease the risk of type II error?