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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.
What test or tests would you use to rule out chance from causing the apparent differences in these data and is there a significant correlation?
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Filtering and Summarizing Data
Define the hypothesis and find the standard error of the difference in the means also find the test statistic - Determine the required sample size to be able to use a 99% confidence interval.
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