What recommendations do you make to the District 1 school board and parents about the difference between the male and female students? 3. (8 points: 2 points for each part) The SPSS dataset math.sav provides data about students' scores on POSTBMTH which represents their performance on a year-end mathematics test and that higher scores demonstrate higher achievement. Suppose that this test was administered to a sample of students enrolled in a local mathematics enrichment program that is being piloted during the school year (they have participated in the program since the beginning of the school year). The researchers know that the mean assessment score for the population of students who are not exposed to special programs such as the one being piloted is equal to 464. The population variance is not known. The researchers would like to formally test whether the sample mean for the program is different than the population mean. a. Specify the null and altemative hypotheses in words and in symbols (statistical notation) that would address this research question. b. Use SPSS and compute an appropriate test statistic to examine the mean difference. Provide the SPSS output. c. Do you reject or accept the null hypothesis and why? What do you conclude? d. What does the 95% confidence interval indicate? Do you accept or reject the null hypothesis and why? What do you conclude? 4. (10 points: 2 points for each part) Using the same dataset math.sav determine whether in mathematics the mean score of males is different than the mean of females. a. Specify the null and altemative hypotheses in words and symbols (statistical notation). b. Use SPSS and compute an appropriate test statistic to examine the mean difference between males and females. Provide the SPSS output