A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following: Determine a 95% confidence interval for the mean amount spent.
A) [45.21, 53.56]
B) [40.36, 58.35]
C) [30.54, 68.14]
D) [45.13, 53.56]
E) [29.34, 69.34]

Question

A manager of a local store wants to estimate the mean amount spent per shopping visit by customers. Summary statistics from a sample taken reveal the following:  Determine a 95% confidence interval for the mean amount spent.
A) [45.21, 53.56] 
B) [40.36, 58.35] 
C) [30.54, 68.14] 
D) [45.13, 53.56] 
E) [29.34, 69.34]

Quizplus · Accepted Answer

Using the formula: 
Mean +/- t(alpha/2, df) * (s/sqrt(n))
where
Mean = 49.385
s = 6.116
n = 30
df = n - 1 = 29

t(alpha/2, df) = t(0.025, 29) = 2.045

Plugging in the values, we get:
49.385 +/- 2.045 * (6.116/sqrt(30))
49.385 +/- 2.045 * 1.117

The resulting 95% confidence interval is [45.13, 53.56]. Therefore, the best choice is D.

A Manager of a Local Store Wants to Estimate the Mean