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.

Observation   A   B
1   793.5   797.9
2   793.6   789.4
3   792.5   795.0
4   793.4   789.5
5   793.4   801.1
6   792.3   790.9

(a) Why are these​ matched-pairs data?

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

B. The measurements​ (A and​ B) are taken by the same instrument.

C. The same round was fired in every trial.

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

​(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 ▼ = 0

H1​: μd ▼ ≠ 0

Determine the test statistic for this hypothesis test.

t0=−0.43

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

Find the​ P-value.

​P-value=__?__

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

Answer 1