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 790.2 790.2 793.3 793.3 791.6 791.6 793.9 793.9 794.7 794.7 793.1 793.1   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​ 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 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​ P-value. ​P-value equals = nothing ​(Round to three 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

790.2

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​ 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 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​ P-value.

​P-value

equals

=

nothing

​(Round to three decimal places as​ needed.)

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