A computer professor is interested in studying the amount of time it would take

Question

A computer professor is interested in studying the amount of time it would take students enrolled in the Introduction to Computers course to write and run a program in Visual Basic. The professor hires you to analyze the following results (in minutes) from a random sample of nine students:

Time

10

13

9

15

12

13

11

13

12

a)     At the 0.05 level of significance, is there evidence that the population average time is greater than 10 minutes? What will you tell the professor?

a.     Hint-- Hypothesis testing for the mean with one sample, and population standard deviation is unknown (z or t hypothesis test??); … is greater… (Upper tail or lower tail, or two tails? watch for your H1: to determine)

b)    Suppose that, when checking her results, the computer professor realizes that the fourth student needed 51 minutes instead of 15 minutes to write and run the Visual Basic program. At the 0.05 level of significance, reanalyze the revised data in part (a). What will you tell the professor?

c)     The professor is perplexed by these paradoxical results and requests an explanation from you regarding the justification for the difference in your findings between (a) and (b). Discuss

d)    A few days later, the professor calls to tell you that the dilemma is completely resolved. The original number 15 was correct, and therefore your finding in (a) are being used in an article she is writing for a computer magazine. Now she wants to hire you to compare the results from that group of Introduction to Computers students against those from a sample of 11 computer science majors, in order to determine whether there is evidence that computer science majors can write a Visual Basic program (on average) in less time than can introductory students. The sample mean for the computer science majors is 8.5 minutes, and the standard deviation is 2.0 minutes. At the 0.05 level of significance, completely analyze these data. What will you tell the professor?

a.     Hint-- Now we have two samples, we want to know if the average time taken by other majors (the data shown in (a), population 1 mean defined as ) is greater than the time taken by computer science major (population 2 mean defined as ) which can be your H1 , H0 : one tail test problem.

e)     A few days later, the professor calls again to tell you that a reviewer of her article wants her to include the p-value for the correct results in (a). In addition, the professor inquires about the unequal variances problem, which the reviewer wants her to discuss in her article. In your own work, discuss the concept of p-value, and describe the unequal variances problem. Give the p-value in (a), and discuss whether the unequal variances problem had any meaning in the professor’s study.

a.      Hint- F test for differences in two variances.

I ONLY NEED TO KNOW D AND E. I HAVE WORKED OUT A-C. THANK YOU IN ADVANCE

Time

10

13

9

15

12

13

11

13

12

Explanation / Answer

d) H0: mu1=mu2

H1: mu1>mu2

t=xbar1-xbar2/pooled var(1/n1+1/n2)

pooled var=n1var1+n2var2/n1+n2-2

n1=9

xbar1=11.111

var1=16.3611

n2=11

xbar2=8.5

var2=sd^2=4

Using excel to test

since p is < 0.05, we reject the null hypothesis and conclude that mu1>mu2.

e) H0: var1=var2

H1: var1 >var2

F=larger var/smaller var=16.36105/4=4.09026

F.DIST.RT(4.0902,8,10) in excle gives the p value as 0.020628

Since p< 0.05, we reject the null hypothesis.

For the test in a) p value is 0.5737

As we reject H0 in a, another sample is taken, so it is true that we need to test for equality of variences. Also as the sample sizes are small, we need to test for the varicnes.

Hypothesis Test: Independent Groups (t-test, pooled variance) sample 1 sample 2 11.111 8.5 mean 4.04488 2 std. dev. 9 11 n 18 df 2.611000 difference (sample 1 - sample 2) 9.493802 pooled variance 3.081201 pooled std. dev. 1.384897 standard error of difference 0 hypothesized difference 1.89 t .0378 p-value (one-tailed, upper)

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