Question

14. A researcher estimates the 95% Confidence Interval for a sample (n=100) with a mean of M=3. The population mean and standard deviation are known as 2.5±2 (µ±σ). What is the upper confidence limit for this interval? A) 0.392 B) 1.96 C) 2.608 D) 3.392 E) There is not enough information to answer this question.

Answer 1

Solution:

Given,

= 2

n = 100

M  = 3   

  Note that, Population standard deviation() is known..So we use z distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96   

The margin of error is given by

E =  /2 * ( / n )

= 1.96 * (2 / 100)

E = 0.392

Now , confidence interval for mean() is given by:

(M  - E ) <   <  (M + E)

(3 - 0.392)   <   <  (3 + 0.392)

2.608 <   < 3.392

Upper confidence limit is 3.392

Answer : 3.392