A random sample of size 16 taken from a normally distributed population revealed a sample mean of 50 and a sample variance of 36.The upper limit of a 95% confidence interval for the population mean would equal:
A)57.81
B)53.20
C)69.90
D)75.31

Question

Quizplus · Accepted Answer

To find the upper limit of the 95% confidence interval, we need to use the formula:

Upper limit = sample mean + (critical value) * (standard error)

The critical value can be found using a t-distribution with degrees of freedom (df) = n-1. For 95% confidence level and df = 15 (16-1), the critical value is 2.131.

The standard error can be calculated as the square root of (sample variance / sample size), which in this case is sqrt(36/16) = 1.5.

Plugging in the values:

Upper limit = 50 + 2.131 * 1.5
Upper limit = 53.20

Therefore, the answer is B.

A Random Sample of Size 16 Taken from a Normally