For a certain nationwide standardized test there are two commonly used preparation products on the market: StudyFocus and Prepara. A researcher in the Education department at a nearby university wants to determine if there is any difference between the two products on the mean score on the test by their users. The researcher obtains the scores on the test from a random sample of 16 users of StudyFocus and a random sample of 15 users of Prepara. (These samples are chosen independently.) For the users of StudyFocus, their sample mean is 498.2 with a sample variance of 12,496.4. For the users of Prepara, their sample OO mean is 605.8 with a sample variance of 1226.5. Assume that the two populations of scores are approximately normally distributed. Can the researcher conclude, at the 0.01 level of significance, that there is a difference between the population mean of the scores on the test by the users of StudyFocus and the population mean of the scores on the test by the users of Prepara? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternate hypothesis H. O Ho : I 1X H : I (b) Determine the type of test statistic to use. (Choose one) 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) X (d) Find the p-value. (Round to three or more decimal places.) (e) At the 0.01 level of significance, can the researcher conclude that there is a difference between the mean score on the test by the users of StudyFocus and the mean score on the test by the users of Prepara? OYes ONO