(Solved): 6. A researcher claims that the mean SAT score is greater than 515. A sample of 1800 students shows ...

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 rescarcher's claim using a \( 0.05 \) significance level. a) State the null and alternative hypothoses. b) Calculate the test statistic (round it to 3 decimal places). e) Find the P-value (round it to 3 decimal places). d) Malae a conclusion based on your answers in parts b) and c). e) Fxplain what would constitute a Type I error in this context. f) Explain what would constitute a Type II error in this context.