Question

2. The College Board reported that the mean SAT score in 2009 was 540 for all US High School students that took the SAT. A teacher believes that the mean score for his students is greater than 540. He takes a random sample of 50 of his students and the sample mean score for the 25 students is 565 with a sample standard deviation of 100. Does he have evidence that his students, on average, do better than the national average?

(a) State the null and alternative hypotheses.

(b) The p-value for the above test was 0.1117. State a conclusion in context of the problem. Use a significance level of 0.05.

(c) A 95% confidence interval for µ is (523.7,606.3). Interpret the confidence interval in context of the problem.

(d) Does your confidence interval support the results of the hypothesis test? Explain.

Answer 1

a) Null and alternative hypotheses

Ho : = 540

H1 : > 540

b) p-value = 0.1117

Decision rule : if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis Ho

Our p-value = 0.1117 > 0.05

Decision : we fail to reject the null hypothesis Ho

Conclusion : There is no sufficient evidence to support the claim that student average SAT score is better than the national average

c) interpretation of confidence interval

We are 95% confident that mean score of all US highschool student that took SAT lies between 523.7 and 606.3

d) given confidence interval does support the claim