Question

Algebra scores in a school district are approximately normally distributed with mean μ = 72 and standard deviation σ = 5. A new teaching-and-learning system, designed to increase average scores, is introduced to a random sample of 36 students, and in the first year the average was 73.5.

(a) What is the probability that an average as high as 73.5 would have been obtained under the old system?

(b) Is the test significant at the 0.05 level? What about the 0.01 level? Explain your answers.

Answer 1

(a)

= 72

= 5

P( >73.5)

P( z > 1.80) = 1- P(z < 1.80) - 1- 0.9641 = 0.0359

(b)

At = 0.05

As the p value (0.0359) is less than level of significance (0.05), we reject the Null hypothesis, i.e.the result is statistically significant. Hence we have sufficient evidence to believe that the mean algebra scores are greater than 72.

At = 0.01

As the p value (0.0359) is greater than level of significance (0.01), we fail to reject the Null hypothesis, i.e.the result is statistically nonsignificant. Hence we do not have sufficient evidence to believe that the mean algebra scores are not equal to 72.