In: Statistics and Probability
Consider the accompanying data on breaking load (kg/25 mm width)
for various fabrics in both an unabraded (U) condition and an
abraded (A) condition.
Use the paired t test to test:
H0: μD = 0 versus
Ha: μD >
0
at significance level 0.01. (Use μD =
μU-A.)
Note: The data below is formatted such that you can copy and
paste it into R.
Fabric | ||||||||
---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
U = c( | 36.5, | 55.0, | 51.2, | 38.7, | 43.2, | 48.8, | 25.6, | 49.6) |
A = c( | 28.5, | 20.0, | 46.0, | 34.0, | 36.5, | 52.5, | 26.5, | 46.5) |
Calculate the mean difference and standard deviation.
d = | |
sd = |
Compute the test statistic value. (Round your answer to three
decimal places.)
t =
p-value =
State the conclusion in the problem context.
Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Fail to reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.
Let us denote the difference
d = U - A
The conclusion in the problem context :
Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.