Question

A teacher has created a better way to do math for improve SAT scores. Based on data from the college board, SAT scores are normally distributed with = 514 and = 113. The teacher finds a sample of 1800 students and puts them through the program. The sample yields a mean SAT math score of M = 518. Use an = 0.10 level of significance to see if the program had any effect. (Please use all procedures for the hypothesis)

Bonus Points (2) What is the p value?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 514
Alternative Hypothesis, Ha: μ > 514

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.282.
Hence reject H0 if z > 1.282

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (518 - 514)/(113/sqrt(1800))
z = 1.5

P-value Approach
P-value = 0.0668
As P-value < 0.1, reject the null hypothesis.

There is sufficient evidence to conclude that A teacher has created a better way to do math for improve SAT scores