Single sample hypothesis testing: z-tests

1. For the population at large, test scores on the Wechsler Intelligence Scale for Children are normally distributed with a mean (μ) of 100 (σ = 15). School district officials wonder whether, on average, the IQ scores of the students in their district differ from the population average. Wechsler IQ scores are obtained for a random sample of 150 of their students, and the mean IQ is found to equal 102. Compute the single-sample z-test to see if there is a difference between the sample and the population. Test the null hypothesis at the .05 level of significance. List your answer in terms of the 6 hypothesis testing steps and provide an explanation of your results in Step 6.

2. Assume that in the population healthy young adults dream an average (μ) of 90 minutes (σ = 10) each night, as inferred from a number of measures, including rapid eye movement. An investigator wishes to determine whether the consumption of coffee just before sleep reduces the amount of dreamtime. After they have consumed a standard amount of coffee, dreamtime is monitored for each of 30 young adults in a random sample. Results show a sample mean, M, of 89 minutes. Compute the single-sample z-test to see if caffeine reduces dreamtime. Test the null hypothesis at the .05 level of significance. List your answer in terms of the 6 hypothesis testing steps and provide an explanation of your results in Step 6.