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	792.6	791.5	793.9	792.2	794.7	794.7
B	794.8	786.9	800.4	791.7	802.3	789.9

​(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 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

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 H 0H0​:

Upper H 1H1​:

Determine the test statistic for this hypothesis test.

t0=

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

Find the​ P-value.

​P-valuee=

​(Round to three decimal places as​ needed.)What is your conclusion regarding

Upper H 0=

α=0.01

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 confidence interval is left parenthesis nothing comma nothing right parenthesis .,.

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

Interpret the confidence interval. Choose the correct answer below.

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

B.One can be​ 99% confident that the mean difference in measurement is 0.01

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

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

​

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

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

B.No, because the boxplot is too large.

C.No, because 0 is not containednot containedin the boxplot.

D.Yes, because the boxplot shows no outliers.

Answer 1

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