Question

The sample size needed to estimate a population mean to within 10 units was found to be 68. If the population standard deviation was 50, then the confidence level used was:

Selected Answer: c. 0.9 Answers: a. 0.99 b. 0.95 c. 0.9 d. 0.85

Answer 1

Margin of error is given by

Given,

E=10

σ =50

n=68

Substituting in (1), we get

Z-value for 90% confidence interval is 1.64

Hence, option (c) is the correct answer

Explanation:

“Critical" values of z are associated with interesting central areas under the standard normal curve.

To any central area there corresponds a “tail area."

Since there are two “tails", the central area is always 1 - (2* tail area)

So, to get a central area of 90%, we need to consider tail area of 5%

90%=1-(2*5%)

Now, Z-value for 5% tail is 1.645

The diagram given below is shared for your reference