Assignment for Chapter 9 (One sample t-test) Find the estimated standard error for the sample mean for each of the following samples. 1. a. n = 25 with SS = 600 b. n = 49 with SS = 960 C. n = 64 with SS 1,134 2. A random sample of n = 12 individuals is selected from a population with μ = 20, and a treatment is administered to everyone in the sample. After treatment, the following scores are observed: 30 28 27 29 30 19 19 22 16 30 32 18 3. 4. a. b. C. d. Compute the sample mean (M) and variance (s²). How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) If there is no treatment effect, what is the typical difference between the sample mean and its population mean? That is, find the standard error of M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) Using a two-tailed test with a = .05, what is your decision? (reject the null or fail to reject the null). To evaluate the effect of a treatment, a sample is obtained from a population with a mean of u = 20, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 22 with a variance of s² = 16. a. b. C. d. e. Assume that the sample consists of n = 9 individuals. Compute the one-sample t. Using a two-tailed test with a = .05, what is your decision? (reject the null hypothesis or fail to reject the null hypothesis) Now assume that the sample consists of n = 25 individuals. Compute the one-sample t. Using a two-tailed test with a = .05, what is your decision? (reject the null hypothesis or fail to reject the null hypothesis) Comparing your answers for parts b and d, how does the size of the sample influence the outcome of a hypothesis test? To evaluate the effect of a treatment, a sample of n = 25 is obtained from a population with a mean of μ=30, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 32. a. b. C. d. e. Assume that the sample variance is s² = 15. Compute the one-sample t. Using a two-tailed test with a = .05, what is your decision? (reject the null hypothesis or fail to reject the null hypothesis) Assume that the sample variance is s² = 50. Compute the one-sample t. Using a two-tailed test with a = .05, what is your decision? (reject the null hypothesis or fail to reject the null hypothesis) Comparing your answers for parts b and d, how does the variability of the scores in the sample influence the outcome of a hypothesis test? 5. Your subjective experience of time is not fixed. You experience time "flying" during some activities and "dragging" during others. Researchers have shown that your experience of time can be altered by drugs that interact with the brain regions that are responsible for timing. Researchers demonstrated that intervals are perceived as longer when under the influence of cocaine. Rats were trained to press Lever 1 after exposure to a short (two-second) sound and Lever 2 after exposure to a long (eight-second) sound. In a later test session, rats under the influence of cocaine were exposed to sounds of different duration and researchers measured lever pressing on Lever 1 and Lever 2. For each rat in the study, the researchers measured the duration of sound in seconds that was equally likely to be judged as long or short. Assume that the untreated population mean is u = 4 seconds and that the sample variance is s² = 0.50, the sample mean is M = 3.50, and the sample size is n = 12. a. b. C. d. e. Compute the one-sample t-test. Report the degrees of freedom and the value of the t. Using a two-tailed test with a .05, what is your decision? (reject the null hypothesis or fail to reject the null hypothesis) Construct the 95% confidence interval to estimate the μ for a population of rats under the influence of cocaine. Calculate the estimated Cohen's d to measure the size of the effect. Calculate r² (the percentage of variance accounted for) to measure the size of the effect.