A consultant working for a State Police barracks contends that service weapons w

Question

A consultant working for a State Police barracks contends that service weapons will fire with a higher muzzle velocity if .the barrel is properly cleaned. A random sample of Glock 9-mm handguns was obtained, and the muzzle velocity (in feet. per second) of a single shot from each gun was measured. Each gun was professionally cleaned, and the muzzle velocity of a second shot (with the same bullet type) was measured. The data are given in the following table. a. What is the common characteristic that makes these data paired? b. Assume normality. Conduct the appropriate hypothesis test to determine whether there is any evidence that a clean gun fires with a higher muzzle velocity. Use alpha = 0.01. c. Find bounds on the p value associates with this hypothesis test.

Explanation / Answer

Part-a

As same gun muzzle velocity is measured before and after the cleaning, so it is paired data as same set of 6 guns used before and after cleaning.

Part-b

We have to test the null hypothesis H0: µd=0 versus the alternative Ha: µd>0

Here alternative is the claim that clear guns fires with a higher muzzle velocity.

From following table results we have

Mean of difference xbar               =15.17

Standard Deviation od difference sd=     74.82

Sample Size n=6

Test statistic t=(xbar-µd)/(s/sqrt(n))

=(15.17-0)/(74.82/sqrt(6))

=0.4966

Degree of freedom =n-1=6-1=5

So right tailed critical t at 0.01 level is =3.365

As calculated t<3.365, we do not reject the null hypothesis and conclude that clear guns do not fires with a higher muzzle velocity.

Part-c

Bound on p-value is 0.25<p<0.50

Gun Before After Difference=After-Before 1 1505 1625 120 2 1419 1511 92 3 1504 1459 -45 4 1494 1441 -53 5 1510 1472 -38 6 1506 1521 15 Mean of difference xbar 15.17 Standard Deviation od difference sd 74.82 Sample Size n 6

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