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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