John Diggle needs to give up his trusted Glock for a more non-lethal weapon. Cisco Ramon builds him a stun gun that his claims matches the Glock shooting characteristics, including accuracy. Do these data representing "shot groups" give statistically significant evidence of a difference in accuracy between the two types?

Glock (cm):

9.3

16.7

7.1

14

5

6

Stun Gun (cm):

4.9

14.1

7

7.2

5.4

8.6

a)Write the Hypotheses:

₁= ₂, the mean difference in accuracy between Glock and Stun Gun is equal

_{1 2}, the mean difference in accuracy between Glock and Stun Gun is different/not equal

b)Are the conditions for inference met? (draw a picture of the histograms)

c)Provide the calculations:

a.Sample mean diff:_________________________________

b.Standard err:_____________________________________

c.T-stat:__________________________________________

d.P-value:_________________________________________

d)Write conclusion:

At the 5% level of significance, we ______________ that the mean difference in ___________ between ____________ and ______________ is _______________. We ________________________ the mean difference in ___________ between ____________ and ______________ is _______________. [P-value = ________ ]

e)Construct a 90% Confidence interval.

f)What does the interval mean in the context of the problem

We are 90% confident that the difference in mean _______________

For ________________________ is between ____________ and _______________ ___________________ than __________________.

g)Was Cisco correct, does John's Stun Gun perform the same? Explain