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	792.8792.8	791.6791.6	791.5791.5	793.1793.1	793.2793.2	793.6793.6
B	797.0797.0	791.3791.3	794.8794.8	790.7790.7	800.8800.8	789.8789.8

Determine the test statistic for this hypothesis test.

Find the​ P-value.

Construct a​ 95% confidence interval about the population mean difference. Compute the difference as device A minus device B. Interpret your results.

Answer 1

HYpothesis;
H0 : mu1-mu2 = 0
HA :mu1 -mu2 not equals to 0

test statistics:

t =(x1 -x2)/sqrt(s1^2/n1+s2^2/n2)
= (792.6333 - 794.0667)/sqrt(0.8779^2/6 + 4.2819^2/6)
= -0.8033

p value = .4584

Do not reject The null hypothesis

t value at 95% = 2.5706

CI = (x1 -x2) +/- t * sqrt(s1^2/n1+s2^2/n2)
= (792.6333 - 794.0667) +/- 2.5706 * sqrt(0.8779^2/6 + 4.2819^2/6)

= ( -1.6110,-1.2558)

we are 95% confident that the population mean difference is between ( -1.6110,-1.2558)