Every year, all incoming high school freshmen in a large school district take a math placement test. For this year's test, the district has prepared two possible versions: Version 1 that covers more material than last year's test and Version 2 test that is similar to last year's test. The district suspects that the mean score for Version 1 will be less than the mean score for Version 2. To examine this, over the summer the district randomly selects 100 incoming freshmen to come to its offices to take Version 1, and it randomly selects 80 incoming freshmen to come take Version 2. The 100 incoming freshmen taking Version 1 score a mean of 112.0 points with a standard deviation of 14.6. The 80 incoming freshmen taking Version 2 score a mean of 118.0 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores from the two versions can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.01 level of significance, is there enough evidence to support the claim that the mean test score, H., for Version 1 is less than the mean test score, ,, for Version 2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H.. O P H : 0 X S p H :I 10 (b) Determine the type of test statistic to use. t Degrees of freedom: 0=0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0-0 030 0>0 X (d) Find the critical value at the 0.01 level of significance. (Round to three or more decimal places.) (e) Can we support the claim that the mean test score for Version 1 is less than the mean test score of Version 2? Yes No