Scenario 1 (z-Test)

According to physician data gathered across the greater Columbus metropolitan area, the average height of 17-year-old girls in the Columbus area is 67 inches, with a standard deviation of 3.19 inches. A high school principle believes the female students in her school are especially tall this year. The teacher records the heights of a random sample of the female students (N = 57) in her school and finds an average of 68.1 inches.

1. Use a two-tailed hypothesis (z) test with alpha = 0.01 to determine if there is any difference in average height of the principle's students and all 17-year-old girls in the Columbus physician database. State the following in your answer: A) Your null and alternative hypotheses in notation and in basic language, B) z-crit, and z-observed, C) Final statistical decision. Interpret your decision in a complete sentence.
2. Calculate a 99% confidence interval. State a decision in regard to the null hypothesis in #1 based on this interval. Interpret your 99% confidence interval.
3. Calculate a 95% confidence interval instead. How is this different than the 99% confidence interval you calculated in #2?
4. Calculate effect size using Cohen's d. Classify the effect size as small, medium, or large AND interpret your result.

Scenario 2 (power)

An industrial-organizational psychologist hypothesizes that assembly line workers would display a higher level of job satisfaction if they were given a new kind of incentive program. He consults the literature on the effect of incentive programs on job satisfaction and predicts that his new program will have a positive, medium effect size (increase of 3.5 points). Assessment of job satisfaction of assembly workers at this company over many years has resulted in a distribution that is approximately normal, with = 82 and = 7 on a standard job satisfaction scale. The psychologist plans to provide the new incentive program to 25 randomly selected assembly workers. If the null hypothesis is tested at a p-level of 0.05 (one-tailed), the power of this study to detect the predicted difference would be 80%.

5. If you were only able to sample 6 individuals (holding all other aspects constant), would power change from 80%? If so, describe HOW and WHY it would change. 6. Based on the original information provided (text before #5), what would be your expectation for power (increase or decrease?) if you lowered the alpha to 0.01? (state your answer AND explain your reasoning) 7. Based on the original information provided (text before #5), what would be your expectation for power (increase or decrease) if you: (state your answer AND explain your reasoning) increased the sample size to 50? 8. Based on the original information provided (text before #5), what would be your expectation for power (increase or decrease) if you ran a 2-tailed test? (state your answer AND explain your reasoning) 9. Based on the original information provided (text before #5), what would be your expectation for power (increase or decrease) if you expected a sample mean of 100? (state your answer AND explain your reasoning) 10. Based on the current example, what would be the best most practical method for maximizing power (beyond 80%) and WHY?

Scenario 3 (1-Sample t-Test)

We know in the U.S. that the population average impulsivity score is 20. A psychologist believes that her clinical patients will obtain impulsivity scores significantly greater than the average. She checks a portion of her patient's impulsivity scores and finds the following scores: 17, 18, 17, 14, 20, 19 Do these patients have significantly higher impulsivity scores than the population average?

1. Identify the populations and state the null and research hypotheses.

Scenario 4 (1-Sample t-Test)

We know that the mean score on a common measure of impulsivity is 20 points. A psychologist believes that the patients in her clinic are significantly different than the average in terms of their impulsivity. She implements impulsivity scale with 30 of her clinic patients and finds the following descriptive statistics: mean = 24.1, variance = 23.717 Do the patients in this sample have significantly different impulsivity scores than the human population average?

1. Identify the populations and state the null and research hypotheses. 1 : ?, 2 : ?, H0: ?, H1: ?
2. State the df and your critical t, based on a p-level of 0.05.
3. Calculate (and report) the t statistic.
4. State your decision and interpret the result. Describe the results in APA format.
5. Calculate the 95% confidence interval for the true population mean.
6. Calculate Cohen's d as a measure of effect size and describe the size of the effect.