The following data represent the muzzle velocity​ (in feet per​ second) of rounds fired from a​ 155-mm 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 790.4 790.7 790.2 792.8 794.3 792.3   B 792.9 786.3 797.9 790.7 803.6 787.5   ​(a) Why are these​ matched-pairs 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 same round was fired in every trial.   D. The measurements​ (A and​ B) are taken by the same instrument. ​(b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the 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=Ai−Bi. Identify the null and alternative hypotheses.   H0​: μd equals=   00 H1​: μd not equals≠   00 Determine the test statistic for this hypothesis test.   t0=    (need this answser) ​(Round to two decimal places as​ needed.)

Question

 

The following data represent the muzzle velocity​ (in feet per​ second) of rounds fired from a​ 155-mm 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
790.4
790.7
790.2
792.8
794.3
792.3
 
B
792.9
786.3
797.9
790.7
803.6
787.5
 
​(a) Why are these​ matched-pairs 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 same round was fired in every trial.
 
D.
The measurements​ (A and​ B) are taken by the same instrument.
​(b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the
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=Ai−Bi.
Identify the null and alternative hypotheses.
 
H0​:
μd
equals=
 
00
H1​:
μd
not equals≠
 
00
Determine the test statistic for this hypothesis test.
 
t0=    (need this answser)
​(Round to two decimal places as​ needed.)

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