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A scientist at a research institute wanted to test a theory thatmarried couples

ID: 2954664 • Letter: A

Question

A scientist at a research institute wanted to test a theory thatmarried couples have the same eating patterns that is, a couple onaverage will eat the same number of sausages. He performed hisexperiment on 4 couples and the data is in a table below. Thenumber of one foot sausages was normally distributed.

Couple

Husband

Wife

1

5

2

2

6

4

3

3

4

4

9

7

a) Does the data suggest that married people have the sameeating patterns? Test using = 0.01

b) Compute a 95% confidence interval for the true meandifference between spouses.

Couple

Husband

Wife

1

5

2

2

6

4

3

3

4

4

9

7

Explanation / Answer

a) Does the data suggest that married people have the sameeating patterns? Test using = 0.01

=0.01, t(0.005,df=n1+n2-2=6)=3.71 (checkstudent t table)

The test hypothesis is

Ho:1=2

Ha:1 not equal 2


The test statistic is

t=(xbar1-xbar2)/(s1^2/n1 +s2^2/n2)

=(5.75-4.25)/sqrt(2.5^2/4 +2.06^2/4)

=0.926


Since t=0.926<3.71, we do not reject Ho. Sothe data suggest that married people have the same eatingpatterns



b) Compute a 95% confidence interval for the true meandifference between spouses.

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