Question

Foot-Length: 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)	difference (d = x − y)
1	272	272	0
2	269	267	2
3	259	261	-2
4	255	254	1
5	261	258	3
6	273	273	0
7	274	270	4
8	258	256	2
9	273	272	1
10	255	253	2
Mean	264.90	263.60	1.30
s	7.99	8.04	1.70

If you are using software, you should be able copy and paste the data directly into your software program.

(a) The claim is that the mean difference is positive (μ_d > 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.
t

_d

=
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

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

reject H₀fail 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

Part a)

This is a right-tailed test.

part b)

Test Statistic :-
S(d) = √(Σ (di - d̅)2 / n-1)
S(d) = √(26.1 / 10-1) = 1.7029
d̅ = Σ di/n = 13 / 10 = 1.3
t = d̅ / ( S(d) / √(n) )
t = 1.3 / ( 1.7029 / √(10) )
t = 2.41

Part c)

P - value = P ( t > 2.414 ) = 0.0195

Part d)

Reject null hypothesis if P value < α level of significance
P - value = 0.0195 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

part e)

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