6. A researcher claims that the mean SAT score is greater than 515. A sample of 1800 students shows the sample mean SAT score is 519 with standard deviation 111. Test the researcher's claim using a 0.05 signicance level. a) State the null and alternative hypotheses. b) Calculate the test statistic (round it to 3 decimal places). c) Find the Pvalue (round it to 3 decimal places). d) Make a conclusion based on your answers in parts b) and c). e) Explain what would constitute a Type I error in this context. f) Explain what would constitute a Type II error in this context