If the population deviation is known and we wish to estimate the population mean with 95% confidence, what is the appropriate critical value z to use?
A) 1.28
B) 1.645
C) 1.96
D) 2.33
E) 2.58

Question

If the population deviation  is known and we wish to estimate the population mean  with 95% confidence, what is the appropriate critical value z to use?
A) 1.28 
B) 1.645 
C) 1.96 
D) 2.33 
E) 2.58

Quizplus · Accepted Answer

When estimating a population mean with a known population standard deviation, we use the z-distribution. 
To calculate the appropriate critical value, we use a 95% confidence level which corresponds to a significance level (α) of 0.05. 
Looking at a standard normal distribution table, the z-score that corresponds to an α of 0.025 (one-tailed) is 1.96. 
Since this is a two-tailed test, we need to find the value that corresponds to an α of 0.025 on both tails, which gives us a critical value of 1.96.

If the Population Deviation Is Known and We Wish