Health Care Research & Statistics Assignment 8B A. The score of individual students on the American College Testing (ACT) Program Composite College Entrance Exam has a symmetric distribution with mean 18.6 and standard deviation of 6. At Redlands High School, 36 seniors take the Exam. Use this information to answer the following questions. 1. The Central Limit Theorem says that the sampling distribution of sample means for this variable will be approximately normal. True or False. 2. The mean of this sampling distribution is _______. 3. The standard error of this sampling distribution is ________. B. The distribution of GPA scores is known to be left skewed. At a large university, a professor took a random sample of 75 students and calculated a 95% confidence interval for the mean GPA at this university. The mean of the sample was 2.97 and the standard deviation was .62. This resulted in the confidence interval 2.83 to 3.11. Use this data to answer the following questions. 1. In calculating the confidence interval we used a t-value rather than a z-value because the standard deviation came from the sample. True or False. 2. If many samples of 75 students were taken and many 95% confidence intervals were calculated, only 5% of the time the sample mean would not be covered one of these intervals. True or False 3. We can say that the probability of the confidence interval covering the true mean is . 95. True or False. 4. If we increased the sample size to 200, the confidence interval would be; Longer, shorter, or the same length 5. If we changed to confidence level to 90%, the confidence interval would be: Longer, shorter, or the same length. 6. If I were to test the hypothesis H0: Mean GPA = 3.10 vs H1: Mean GPA 3.10 at the 5% level of significance, I would Fail to reject the null hypothesis. True or False 7. If I were to test the hypothesis H0: Mean GPA = 3.20 vs H1: Mean GPA >3.20 at the 5% level of significance, I would reject the null hypothesis based on this confidence interval. True or False. C. A company that helps students improve their test score on college entrance tests advertises that the study program increases a person's score on the ACT test by a mean of 4 points. A consumer group wishes to test whether the mean increase in score differs from 4 points. The level of significance of their test is 5% and the computer output for the test gives a p-value of .08. 1. State the null hypothesis is symbols: _________ 2. State the alternative hypothesis in symbols: _______ 3. 4. Based on the p-value from the computer output, I should: Reject the null hypothesis or Fail to reject the null hypothesis. What would be the p-value, if the alternative hypothesis was one-tailed: ______. D. Twelve runners were asked to run a 10 kilometer race on each of two consecutive weeks. In one of the races the runners wore one brand of shoe and in the other race a different brand of shoe. The brand of shoe they wore in each race was determined at random. All runners were timed and the results in minutes were recorded for comparison. 1. Which statistical test should be used to analyze the data: Paired t-test, or Independent t-test. 2. What type of test should the researchers do? One-tailed or two-tailed. 3. How many degrees of freedom are there for the t-statistic used in this test? _____ 4. If the critical value for the t-statistic from the table is 2.201 and the value of t calculated from the data was 2.54, what should you do? Reject the null hypothesis or fail to reject the null hypothesis. 5. If the conclusion in #4 is incorrect, what type of error will the researchers have made? Type I or Type II E. A researcher wishes to compare the mean amount of time (in hours) spent in extracurricular activities by high school students in a big city and in a nearby suburb. The research took random sample of size 30 from each of the groups. 1. Which statistical test should be used to analyze the data? Paired t-test or Independent t-test. 2. How many degrees of freedom are there for the t-statistic used in this test? _____ 3. If the critical value for the t=statistics from the table is 2.048 and the t calculated from the data is 1.92, what should you do? Reject the null hypothesis or fail to reject the null hypothesis? 4. If the conclusion is #3 is incorrect, what type of error will the researches make? Type I or Type II. F. What does statistically significant mean? G. What does \"clinically important\" or :\"important in the content area\" mean? ---Extra points: The Central Limit Theorem Quiz If the original population has mean 30 and standard deviation 16, the sampling distribution of sample means for samples of size 25 will have mean ________ and standard error ________? T- Distribution If we have a sample of size 15 and are using the t-distribution, the number of degrees of freedom we need to use is________