Question

To decide whether chemistry or physics majors have higher starting salaries in the industry. n B.S. graduates of each major are surveyed, yielding the following results (in $1000’s):

Major	Sample Average	Sample SD
Chemistry	41.5	2.5
Physics	41.0	2.5

Calculate the P-value for the appropriate two-sample t test, assuming that the data was based on n = 100. Then repeat the calculation for n = 400. Is the small P-value for n = 400 indicative of a difference that has practical significance? Would you have been satisfied with just a report of the P-value? Comment briefly.

Answer 1

Answer:

Given,

Ho : u1 - u2 = 0

Ha : u1 - u2 > 0

test statistic z = (x - u)/sqrt(s1^2/n1 + s2^2/2)

substitute values

= (41.5 - 41)/sqrt(2.5^2/100 + 2.5^2/100)

= 1.414

P value = P(z > 1.414)

= 0.078681 [since from z table]

= 0.0787

Here we observe that, p value > alpha, so we fail to reject the Ho.

So there is no sufficient evidence to support the claim.

Now for sample 400

i.e.,

test statistic z = (41.5 - 41)/sqrt(2.5^2/400 + 2.5^2/400)

= 2.828

P value = P(z > 2.828)

= 0.002342 [since from z table]

= 0.00234

Here we observe that, p value < alpha, so we reject the Ho.

So there is sufficient evidence to support the claim.