Question

The registrar claims that the mean IQ of students at Stetson University (μ_0) is 120 with a standard deviation (σ) of 10. You obtain a random sample of 25 students and find that their mean (X ̅ ) is 115.State the null and alternative hypotheses. Conduct a z test to evaluate the registrar’s claim. Let α=.05. Please show your work and be sure to provide the z statistic, critical z value, and p value. What decision do you make about the null hypothesis? How do you know? Then, write a statement to interpret the results

Answer 1

The null and alternative hypothesis are

H0: = 120

Ha: 120

Test statistics

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

= ( 115 - 120) / (10 / sqrt(25))

= -2.5

Critical z value = -1.96 , 1.96 ( From Z table)

p-value = 2 * P(Z < z) (Since this is two tailed test, we multiply probability by 2)

= 2 * P(Z < -2.5)

= 2 * 0.0062

= 0.0124

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

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