please write out and show all work clearly

Last year, the national mean on the SAT Math test was 514. In order to recruit more students, The Stanley Academy High School is claiming that their students score higher than the national average on the SAT Math test. In order to test this claim, a random sample of 50 SAT Math test scores from Stanley Academy students are listed on the next page. Use the scores to test the claim that the mean test score for all Stanley Academy students is greater than 514 (thus, testing that the mean SAT Math score for Stanley Academy Students is greater than the national average). 1. State the claim, null hypothesis, and alternate hypothesis in symbols. Claim: Ho: H1 : 2. Copy and paste the sample of 50 Stanley Academy SAT math test scores into one column in stat crunch. Calculate the mean and standard deviation for the sample. (Stat > Summary Stat > Columns) x =/ S : 3. Use stat crunch to run a hypothesis test for mean. Go to stat > t-stats > one- sample > with summary Enter information about your sample. Enter your information for your null hypothesis and alternative hypothesis (make sure to select the appropriate inequality sign for your alternate hypothesis). Record your p-value: 4. Based on your p-value, do you reject your null hypothesis or fail to reject your null hypothesis? Use a 0.05 significance level. 5. Based on your answer to #4, does the sample data provide evidence that Stanley Academy has SAT Math test scores that are higher than the national average (greater than 514)? Is it fair for Stanley Academy to be claiming their test scores are higher than the national average? 660, 490, 550, 560, 450, 500, 430, 390, 680, 660, 360, 570, 500, 630, 570, 550, 520, 550, 400, 520, 450, 510, 440, 450, 530, 510, 490, 550, 500, 500, 480, 610, 660, 460, 650, 500