For each problem, conduct the appropriate inferential test using hypothesis testing steps: A. Please state both the null and alternative hypotheses. B Select a significance level C. Please show all calculations needed to generate the appropriate statistic. D. State your decision as to whether the investigator should reject die null hypothesis. E. Calculate the effect size for each problem. 1. The mean Verbal SAT score for the population of first students at Radford is 520. The standard deviation of scores in this population is 95. An investigator believes that the mean Verbal SAT of first year psychology majors is significantly different from the mean score of the population. The mean of a sample of 36 first year psychology majors is 548. Please test the investigator's prediction using an alpha level of .05. 2. The mean Verbal SAT score for the population of first students at Radford is 520. An investigator believes that the mean Verbal SAT of first year psychology majors is significantly greater than the mean score of the population. The mean of a sample of 25 first year psychology majors is 548. The standard deviation of scores in this sample is 95. Please test die investigator's prediction using an alpha level of .05. 3. An investigator thinks that people under the age of forty have vocabularies that are different than those of people over sixty years of age. The investigator administers a vocabulary test to a group of 31 younger subjects and to a group of 31 older subjects. Higher scores reect better performance. The mean score for younger subjects was 14.0 and the standard deviadon of younger subject's scores was 5.0. The mean score for older subjects was 20.0 and the standard deviation of older subject's scores was 6.0. Does this experiment provide evidence for the investigator's theory? Are these results meaningful? 4. An investigator theorizes that people who participate in a regular program of exercise will have levels of systolic blood pressure that are significantly different from that of people who do not participate in a regular program of exercise. To test this idea the investigator randomly assigns 21 subjects to an exercise program for 10 weeks and 21 subjects to a nonexercise comparison group. After ten weeks the mean systolic blood pressure of subjects in the exercise group is 137' and the standard deviation of blood pressure values in the exercise group is 10. After ten weeks, the mean systolic blood pressure of subjects in the nonexercise group is 127 and the standard deviation on subjects in die non-exercise group is 9.0. Please test the investigator's theory using an alpha level of .05. Additionally, determine the correlation between the exercise program and blood pressure. 5. An investigator believes he has developed and intelligence stimulator (Smart Pill!) and wants to test his new drug. The investigator selects 5 participants to take an IQ test, then begin using this Smart Pill daily for one week. Each participant retakes the IQ test. IQ scores are listed below: PrePill: 98, 110, 103, 100, 125 PostPill: 110, 112, 115, 120, 120 Does the Smart Pill increase intelligence
