2. (14 points) Test preparation companies claim that their coaches can raise SAT scores of high school students. A rando

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2 14 Points Test Preparation Companies Claim That Their Coaches Can Raise Sat Scores Of High School Students A Rando 1 (113.47 KiB) Viewed 23 times

2. (14 points) Test preparation companies claim that their coaches can raise SAT scores of high school students. A random sample of 310 students who took the SAT twice included 154 students who were not coached before their first SAT attempt but were coached before their second attempt. The sample also included 156 students who were uncoached for either attempt. Students who retake the SAT without coaching typically raise their scores, so we can test the claim that coaching can improve a student's SAT score. The table below summarizes gains in SAT Verbal scores between the first and second attempt for each group of students (for example, the sample mean gain in SAT Verbal scores for the 154 students who were coached after their first attempt was 26.51 points, with a sample standard deviation of 9.67) Gain in SAT Verbal scores (in points) Ý Coached 154 26.51 9.67 Uncoached 156 24.98 9.68 S n b. Use the provided information to perform a two-sample t-test to determine whether the medn gain in SAT Verbal scores is higher for students who were coached after their first attempt. a. State the null and alternate hypotheses. Use us to represent the population mean gain in SAT Verbal scores for the "Coached" group and use plz to represent the population mean gain in SAT Verbal scores for the "Uncoached" group. Be sure to use correct notation and symbols. Is this this this a two-sided test or a one-sided test? Explain why. c. You can assume that the conditions are met for this hypothesis test. Calculate the test statistic for this hypothesis test using the appropriate formula. YOU MUST SHOW ALL WORK IN YOUR DOCUMENT TO RECEIVE FULL CREDIT. Round your final answer to three decimal places Determine the p-value for this hypothesis test using the STAT100 Z Table. Use correct notation and state the p-value as a decimal rounded to four decimal places. Draw a conclusion for this hypothesis test and give the reason for your conclusion. Use a level of significance of a = .05. Draw a conclusion for this hypothesis test and give the reason for your conclusion but use a level of significance of a =.10. Did you have the same conclusion for this hypothesis test under the two different levels of significance (for a = .05 and a = 10)? If not, provide the value of a test statistic (not a p- value) that would result in the same conclusion for this hypothesis test under the two different levels of significance. d. e. f. 8.