Question

2. a. Use signifcance test to test the indicated claim. A standard aptitude test is given to several randomly selected programmers, and the scores are given below for the mathematics and verbal portions of the test. At the 0.05 level of significance, test the claim that programmers do better on the mathematics portion of the test.

               Mathematics 447 540 427 456 527 449 477 498 425         

               Verbal                    385 478 343 371 440 371 394 422 385

b. Find a 90% confidence interval for the difference of the mean.

Answer 1

Here we have data:

Mathematics	Verbal
447	385
540	478
427	343
456	371
527	440
449	371
477	394
498	422
425	385

Excel output for hypotheses test:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	471.7777778	398.7777778
Variance	1749.194444	1696.444444
Observations	9	9
Hypothesized Mean Difference	0
df	16
t Stat	3.730862424
P(T<=t) one-tail	0.00090991
t Critical one-tail	1.745883676
P(T<=t) two-tail	0.001819821
t Critical two-tail	2.119905299

a) Hypotheses

H_o: μ₁ = μ₂

H_a: μ_{1 >}μ₂

Test statistics :

t = 3.73

Critical value:

t-critical = 1.75

Conclusion: Reject the null hypothesis, here we have sufficient evidence to reject the null hypothesis because t-observed value (3.73) is grater than t-critical value (1.75). We can say that mathematics portion is batter than verbal.

b)