Question

Use t distribution to answer this question:

2. Medical schools A and B reported the following summary of MCAT (Medical Aptitude Test) verbal scores. Test the claim that the applicants of Medical school A score higher than their counterparts of Medical school B. (a) At α = 5%, use the Classical approach to conclude it. (b) Using the P-value approach to conclude it.

Medical school A : n=16, X bar=420, S²= 144

Medical school B : n=8, X bar=408,S²= 128

Answer 1

a) H₀:

    H₁:

The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                             = (420 - 408)/sqrt(144/16 + 128/8)

                             = 2.4

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

      = (144/16 + 128/8)^2/((144/16)^2/15 + (128/8)^2/7)

      = 15

At 5% significance level the critical value is t_{0.95, 15} = 1.753

As the test statistic value is greater than the critical value ( 2.4 > 1.753), we should reject the null hypothesis.

So there is sufficient evidence to support the claim that the applicants of Medical school A score gigher than their counterparts of Medical school B.

b) The P-value = P(T > 2.4)

                        = 1 - P(T < 2.4)

                        = 1 - 0.9851

                        = 0.0149

As the P-value is less than the significance level (0.0149 < 0.05), we should reject the null hypothesis.

So there is sufficient evidence to support the claim that the applicants of Medical school A score gigher than their counterparts of Medical school B.

                          OK