Question

We draw a random sample of size 36 from a population with standard deviation 3.2. If the sample mean is 27, what is a 95% confidence interval for the population mean?

[26.7550, 28.2450]

[25.9547, 28.0453]

[25.8567, 28.1433]

[26.8401, 27.1599]

Answer 1

= Solution :

Given that,

Point estimate = sample mean = = 27

Population standard deviation =    = 3.2

Sample size n =36

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.96 * (3.2 /  36 )

= 1.0453
At 95% confidence interval estimate of the population mean
is,

- E < < + E

27-1.0453 <   < 27+ 1.0453

[25.9547, 28.0453]