The following data represent the muzzle velocity (in feet persecond) 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
790.2790.2
791.3791.3
791.4791.4
793.7793.7
793.4793.4
793.3793.3
B
800.1800.1
789.7789.7
799.8799.8
792.6792.6
802.1802.1
788.5788.5
(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.
