Question

During a discussion among College Board educators, one researcher claimed that SAT Math (SATM) scores overestimate the abilities of typical NY HS seniors since only a minority of HS seniors takes the test. One researcher claims that the true mean SATM score should be no more than 450. The researcher then attempts to test the claim by administering the SATM to a simple random sample (SRS) of 500 NY HS seniors. The mean for the sample was 461. The standard deviation for SAT scores is 100. Discuss the results of the study using a null hypothesis test. What do you conclude?

Answer 1

H₀: < 450

H₁: > 450

The test statistic z = ()/(s/)

                            = (461 - 450)/(100/)

                            = 2.46

At alpha = 0.05, the critical value is z_0.95 = 1.645

Since the test statistic value is greater than the critical value (2.46 > 1.645), so should reject the null hypothesis.

So at 5% significance level there is not sufficient evidence to support the claim that the true mean SATM score should be no more than 450.