Question

1. We take a sample of 119 gun owners in Prince George’s county and ask them how many days in a month they carry a gun on their person. The sample mean is 2.1, with a standard deviation of 1.3. Construct a 91% confidence interval around the sample mean and interpret it.

What would happen to our confidence interval if it we increased our confidence level from 91% to 96%? Why?

What would happen to our confidence interval if we increased our sample size to 1000? Why?

Answer 1

mean = 2.1 and sd = 1.3
n = 119

SE = 1.3/sqrt(119) = 0.1192
z-value = 1.6954

ME = 1.6954*0.1192 = 0.2021

91% CI = (2.1 - 0.2021, 2.1+0.2021)
= (1.8979, 2.3021)

One can be 91% confident that the mean of the 119 sample taken from the population lies in the above interval

If we increase the CI to 96%, z-value will increase and this will lead to increase in ME which in turn lead to increase in the lower and upper limits of CI. In short, CI will increase.

If sample size increase to 1000, SE will decrease and hence the ME. Hence, CI will decrease.