The following data represent the muzzle velocity (in feet per second) of rounds fired from a 155mm gun. For each round, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data. Complete parts (a) through (d) below.
Observation 
1 
2 
3 
4 
5 
6 

A 
790.2 790.2 
793.3 793.3 
791.6 791.6 
793.9 793.9 
794.7 794.7 
793.1 793.1 

B 
794.8 794.8 
789.0 789.0 
796.2 796.2 
793.5 793.5 
802.9 802.9 
791.3 791.3 
(a) Why are these matchedpairs data?
A.
All the measurements came from rounds fired from the same gun.
B.
Two measurements (A and B) are taken on the same round.
Your answer is correct.
C.
The measurements (A and B) are taken by the same instrument.
D.
The same round was fired in every trial.
(b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the
alpha equals 0.01
α=0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Let di
equals
=Ai
minus
−Bi. Identify the null and alternative hypotheses.
Upper H 0
H0:
mu Subscript d
μd
equals
=
0
0
Upper H 1
H1:
mu Subscript d
μd
not equals
≠
0
0
Determine the test statistic for this hypothesis test.
t0
equals
(Round to two decimal places as needed.)
Find the Pvalue.
Pvalue
equals
=
nothing
(Round to three decimal places as needed.)
a.
From the provided information, the two measurements (A and B) are taken on the same round. Therefore, these are matched pair data.
Thus, option B) is correct.
b.
The difference table between the data can be obtained as:
The mean and standard deviation of difference can be obtained as:
The null and alternate hypothesis can be constructed as:
Null hypothesis, H0:µd=0. (There is no significance difference in the measurement of velocity.)
Alternative hypothesis, H1:µ...
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