1. (10 points: two points for each part) A math test was administered to a sample of 41 eighth grade students, at the end of the eighth grade, who had enrolled in a special enrichment program since the beginning of the school year. Suppose that the population standard deviation is 100, and the sample mean is 470.174. The researcher is interested in comparing the sample mean and the population mean of the untreated population (which is 440}. a. State the Null Hypothesis in words and symbols (statistical notation) and the Alternative Hypothesis in words and symbols (statistical notation). b. Construct a test statistic to determine whether the mean difference is statistically signicant. c. Determine the pvalue of the test statistic. d. Given the result in b do you accept or reject the null hypothesis and why? What do you conclude? Provide a substantive interpretation. e. Compute 95% and 99% condence intervals around the sample mean of 470.174. Do you reject or accept the null hypothesis and why? What do you conclude? 2. (18 points) The district 1 school board has been approached by a group of parents concerned about their fourth grade students' performance. Specically, they are concerned that District 1 students are not performing at the same level as the population of fourth grade students in the state. Additionally, the parents are concerned about the academic performance of female students vis a vis the performance of their male peers in the 4th grade. Suppose the outcome of interest is English. Assume that the population parameters for English (the mean and the standard deviation of the mean) in total and for each gender separately are as follows