Question

It has been claimed that, on average, right-handed people have a left foot that is larger than the right foot. Here we test this claim on a sample of 10 right-handed adults. The table below gives the left and right foot measurements in millimeters (mm). Test the claim at the 0.05 significance level. You may assume the sample of differences comes from a normally distributed population.

Person	Left Foot (x)	Right Foot (y)
1	268	268
2	265	263
3	255	257
4	251	250
5	257	254
6	269	269
7	269	266
8	254	252
9	269	268
10	251	249

You should be able copy and paste the data directly into your software program.

(a) The claim is that the mean difference (x - y) is positive (μd > 0). What type of test is this?

This is a right-tailed test.

This is a two-tailed test.    

This is a left-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.

td =

(c) What is the P-value of the test statistic? Round to 4 decimal places.

P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H0

fail to reject H0    

(e) Choose the appropriate concluding statement.

The data supports the claim that, on average, right-handed people have a left foot that is larger than the right foot.

There is not enough data to support the claim that, on average, right-handed people have a left foot that is larger than the right foot.    

We reject the claim that, on average, right-handed people have a left foot that is larger than the right foot.

We have proven that, on average, right-handed people have a left foot that is larger than the right foot.

Answer 1

Since we have a small sample, we would be using a t-test for difference of means.

The statistical theory behind the test can be seen in the pic below:

In the given problem,

a) This is a right tailed test, because we have x-y>0.

b) t test statistic: 0.337170

c) p-value: 0.369943

d) conclusion regarding H0:

Since p value > level of significance, we accept H0 at 5% level of significance.

we fail to reject Ho

e) Concluding statement

There is not enough data to support the claim that, on average, right-handed people have a left foot that is larger than the right foot.    

Therefore we can say that both the samples belong to the same population, and hence there is no difference between left foot size and right foot size.