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Chapter 8

The Comparison of Two populations

Assignment 8

Q1. An auto racing driver is given training and his timings on five different tracks are then measured. The times before and after training are given below. Is the training beneficial to the driver? The differences are taken as after - before. ( 2.5 points)


a) State the null and alternative hypothesis to test that the training was beneficial to this driver.

H0: μD ≥ 0

H1: μD<0

What is/are the critical value(s) of the test at alpha equal to 0.01?

The critical value is2.326

b) Compute the test statistic. 

D= -20.4

D1=-28 D2=-5 D3=30 D4=-83 D5=-16

Sd =√(784+25+900+6883+256)/4 =47

T= (-20.5-0)/21 =-0.9762

P= 0.5-0.33 = 0.17

c) State your conclusion.

Reject H0. Calculated Z value is smaller than the critical value of Z. Note that the null hypothesis would be rejected at any conventional level of significance.

d) Was the training beneficial to this driver?

NO ,the training is not beneficial to this driver

Q2. A major educational testing service is evaluating the performance of its new automated essay grading system. Student essays are scanned into a computer-recognizable format and then evaluated by the computer program. The software will not be moved into second-level testing unless there is compelling evidence that it finds more grammatical errors than human graders.

A random sample of 100 essays evaluated by the software was compared to a different sample of 100 essays evaluated by humans. Results were as follows:


It is assumed that both software grading (population 1) and human grading (population 2) are normally distributed, with equal population variances. Test at alpha equal to 0.05. (2.5 points)

a) State the null and alternative hypotheses to test whether this software does pick out more errors.

H0: μ1 - μ2 ≥ 0

H1: μ1 - μ2 < 0

b)  What is/are the critical value(s) of the test.?

alpha equal to 0.05 , the critical value...