For the following, a) identify null and alternative hypotheses, b) find the critical value(s) and identify the rejection region(s), c) find d and sa d) use the t-test to calculate the standardized test statistic, d) decide to reject or accept the null hypothesis, and e)Write an APA format results statement. Assume that the distribution of the population is approximately normal. An SAT prep course claims to improve the test scores of students. The table shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her score. Test the claim at a = 0.01. Student First SAT 2 3 4 5 6 7 308 456 352 433306 471 422| Second SAT|400524 409 491 348 583 451 1

a. set up appropriate null and alternative hypotheses of the test b. choose an appropriate test statistic and use the data to find the p-value

You wish to test the following claim (Ha) at a significance level of a = 0.02. H.:µ1 – µ2 =0 Ha:µ1 – P2 > 0 || You obtain the following two samples of data. Sample #2 Sample #1 61.3 63.5 47.7 51.2 52 39.2 59.7 53.3 54.7 51 54.2 45.5 55.6 46.6 65.3 33 54 48.4 46.6 49.2 65.8 58.6 53.4 49.4 54 54.7 67.7 41.4 47.1 46.1 34 55.4 57.7 55.5 40.7 54.2 Do not test the sample variances using Fcdf. Assume the sample variances are not equal and DO NOT POOL. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value = The p-value is... Oless than (or equal to) a Ogreater than a

A. Suppose we want to test whether or not three means are equal. We want to perform this test with a 8% significance level.If we perform an ANOVA test, what is the probability of the test producing accurate results (avoiding a Type I error)? B. Suppose we, instead, run three separate hypothesis tests (t-tests), each with 8% significance level. Mean 1 = Mean 2Mean 1 = Mean 3Mean 2 = Mean 3What is the probability that all three tests would be accurate? C. Why is an ANOVA test more accurate than 3 different tests?