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	791.9	794.6	794.2	794.1	793.8
B	796.1	787.0	803.4	792.6	794.8	791.0

a) Why are these​ matched-pairs data?

A. Two measurements​ (A and​ B) are taken on the same round.

B. All the measurements came from rounds fired from the same gun.

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 0.01α=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.

Upper H0​: μd ▼(<, =, > ,≠) ________ , ________

H1​:μd▼(s≠, >, =, <) ________ , ________

Determine the test statistic for this hypothesis test.

t0=________ ​(Round to two decimal places as​ needed.)

Find the​ P-value.

​P-value=_________ ​(Round to three decimal places as​ needed.)

What is your conclusion regarding

Upper H 0H0​? ▼ (Reject, Do not reject) There ▼(is, not) is sufficient evidence at the α=0.010.01 level of significance to conclude that there is a difference in the measurements of velocity between device A and device B.

(c) Construct a​ 99% confidence interval about the population mean difference. Compute the difference as device A minus device B. Interpret your results.

The lower bound is ________.

The upper bound is _______ . ​(Round to two decimal places as​ needed.)

Interpret the confidence interval. Choose the correct answer below.

A. One can be​ 99% confident that the mean difference in measurement lies in the interval found above.

B. One can be​ 1% confident that the mean difference in measurement lies in the interval found above.

C. One can be​ 99% confident that the mean difference in measurement is 0.

D. One can be​ 99% confident that the mean difference in measurement is0.01.

d) Draw a boxplot of the differenced data.

Does this visual evidence support the results obtained in part​ (b)?

A. ​Yes, because 0 is contained in the boxplot.

B.​Yes, because the boxplot shows no outliers.

C.​No, because the boxplot is too large.

D.​No, because 0 is not contained in the boxplot.

Answer 1

a)

A. Two measurements​ (A and​ B) are taken on the same round.

b)

Following table shows the calculation for difference, its mean and standard deviation:

A	B	d=A-B	(d-mean)^2
790.4	796.1	-5.7	22.250089
791.9	787	4.9	34.609689
794.6	803.4	-8.8	61.105489
794.2	792.6	1.6	6.671889
794.1	794.8	-0.7	0.080089
793.8	791	2.8	14.311089
Total		-5.9	139.028334

Sample size: n=6

We cannot conclude that there is a difference in the measurements of velocity between device A and device B.

(C)

The lower bound is -9.66.

The upper bound is 7.70. ​(Round to two decimal places as​ needed.)

Interpret the confidence interval. Choose the correct answer below.

A. One can be​ 99% confident that the mean difference in measurement lies in the interval found above.

(d)

A. ​Yes, because 0 is contained in the boxplot.