# Statistics for the behavior sciences

7.22
Using the z table in Appendix B, Calculate the following percentages for a z score of -0.08
Above the z score
Below the z score
At least as extreme as this z score
7.32
If the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases:
z= -0.94
z=2.12
A z score for which 49.6% of the data fall between z and the mean
7.36
Assume that the following set of data represents the responses of 10 participants to three similar statements. The participants rated their agreement with each statement on a scale from 1 to 7.

7.40
Height and the z statistic: Imagine a basketball team comprised of thirteen 15 year old boys. The average height of the team is 69.5 inches. Remember, ?=67 inches and s=3.19 inches
calculate the z statistic
How does the sample of boys compare to the distribution of sample means?
What is the percentile rank for this sample?

7.58
You have just conducted a study testing how well two independent variables, daily sugar intake (as assessed by a 25-item eating habits scale) and physical activity (as assessed by a 20-items daily physical activity scale), predicted the dependent variable of blood sugar levels. There were only 17 participants to start with, and 3 of them dropped out before having their blood sugar levels. There were only 17 participants to start with, and 3 of them dropped out before having their blood sugar levels assessed. In addition, 2 participants left one item blank on the physical activity scale, and 4 other participants left most of the data on the eating habits scale blank. At their debriefing interview, they said they just couldn?t estimate food intake with any accuracy.

What will you do with the data of the 3 participants who dropped out just before having their blood sugar levels assessed?
What are your options with regard to the data from the 2 participants who did not respond to most of the items on the eating habits scale?
What are your options with regard to the data from the 4 participants who did not respond to most of the items on the eating habits scale?
Do you recommend using these data at all? If so, how?

8.22
In 2008, the Gallup poll asked people whether or not they were suspicious of steroid us among Olympic athletes. Thirty-five percent of respondents indicated suspicion when they saw an athlete break a track-and-field record, with a 4% margin of error. Calculate an interval estimate

8.32
Calculate the standard error for each of the following sample sizes when ?=1014 and s=136:
12
39
188

8.46
Cheating with hypothesis testing: Unsavory researchers know that one can cheat with hypothesis testing. That is, they know that a researcher can stack the deck in her or his favor, making it easier to reject the null hypothesis.
if you wanted to make it easier to reject the null hypothesis, what are three specific things you could do?
Would it change the actual difference between the samples? Why is this a potential problem with hypothesis testing?
8.48
Confidence intervals, effect sizes, and tennis serves: Let?s assume the average speed of a serve in men?s tennis is around 135 mph, with a standard deviation of 6.5 mph. Because these statistics are calculated over many years and many players, we will treat them as a population parameters. We develop a new training method that will increase arm strength, the force of the tennis swing, and the speed of the serve, we hope. We recruit 9 professional tennis players to use our method. After 6 months, we test the speed of their serves and compute an average of 138 mph.

Using a 95% confidence interval, test the hypothesis that our method makes a difference
Compute the effect size and describe its strength.
Calculate statistical power using an alpha of 0.05, or 5%, and a one-tailed test.
Calculate statistical power using an alpha of 0.10, or 10%, and a one-tailed test.
Explain how power is affected by alpha in the calculations in parts (c) and (d).

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