Question

3. Gun owners in McDonough County were asked how many days in a month they typically carry a gun on their person. The sample size of gun owners was 119, with a mean of 2.1 and standard deviation of 1.3. Construct a 95% confidence interval around the sample mean and interpret it. (5 points)

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 2.1

Population standard deviation =   $\sigma$ = 1.3

Sample size = n =119

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96   ( Using z table )

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

=1.96 * (1.3 /  $\sqrt$119 )

E= 0.2336
At 95% confidence interval estimate of the sample mean
is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

2.1 - 0.2336 <  $\mu$ < 2.1+ 0.2336

1.8664 <  $\mu$ < 2.3336

( 1.8664 , 2.3336 )

At 95% confidence interval estimate of the sample mean ( 1.8664 , 2.3336 )