Question

The random variable X has mean μ and standard deviation σ. A simple random sample of 50 values drawn from X has sample mean 14.7. Assuming the standard deviation is known to be 3.6, construct an 98% confidence interval for the value of μ. Put your answer in correct interval notation, (lower bound, upper bound), and round to three decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean =   = 14.7

Population standard deviation =    = 3.6

Sample size = n =50

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * (3.6 /  50 )

E= 1.1842
At 98% confidence interval estimate of the population mean
is,

- E < < + E

14.7 - 1.1842 <   < 14.7+ 1.1842

13.5158<   < 15.8842

( lower bound =13.516, upper bound=15.884)