Question

iQ scores are normally distributed with a mean of 100 and an sd of 20. I want to test to see if Snow college students have higher IQs than the average. I take a RANDOM sample of 40 students and they average 106 pts. Conduct a full hypothesis test to see if Snow students have higher IQ's than average

Answer 1

H0: = 100

Ha: > 100

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 106 - 100) / ( 20 / sqrt(40) )

= 1.90

p-value = P(Z > z)

= P(Z > 1.90)

= 1 - P(Z < 1.90)

= 1 - 0.9713

= 0.0287

Since p-value < 0.05 significance level, Reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim.