Question

a. A random sample of 25 is taken from a normal distribution with population mean = 62, and population standard deviation = 7. What is the margin of error for a 90% confidence interval?

b. Repeat the last problem if the standard deviation is unknown, given that the sample standard deviation is S=5.4

Answer 1

a) here, n=25 , = 62 , = 7

Here, since the population standard deviation is known we use a z distribution. Z value for 90% confidence level is 1.645.

Margin of error = z*/n

= 1.645 * 7/ 50

= 1.628

b) Here, s = 5.4

Here, since the population standard deviation is unknown we use the t distribution.

Degrees of freedom = n-1 = 24

Critical value of t with df = 24 at 90% confidence level = 1.711

Margin of error = t*s/n

= 1.306