Question

The mean SAT score in mathematics, μ, is 513. The standard deviation of these scores is 48. A special preparation course claims that its graduates will score higher, on average, than the mean score 513. A random sample of 150 students completed the course, and their mean SAT score in mathematics was 519. At the 0.01 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 48

Answer 1

x̅ = 519, σ = 48, n = 150

Null and Alternative hypothesis:

Ho : µ = 513

H1 : µ > 513

Critical value :

Right tailed critical value, z crit = ABS(NORM.S.INV(0.01) = 2.326

Reject Ho if z > 2.326

Test statistic:

z = (x̅- µ)/(σ/√n) = (519 - 513)/(48/√150) = 1.5309

p-value :

p-value = 1- NORM.S.DIST(1.5309, 1) = 0.0629

Decision:

p-value > α, Do not reject the null hypothesis

Conclusion:

There is not enough evidence to conclude mean is greater than 513 at 0.01 significance level.