Question

Assume the population has a normal distribution. A sample of 1250 college and university seniors has an average GPA of 2.5 and a standard deviation of 0.5.

Construct a 96% confidence interval for the population mean, μ

Group of answer choices

.247 to .253

2.47 to 2.53

2.52 to 2.61

2 to 3

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 2.5

Population standard deviation =     = 0.5

Sample size n =1250

At 96% confidence level the z is ,

Z / 2   = Z0.02 = 2.05 ( Using z table )

Margin of error = E =   Z / 2     * ( /n)
= 2.05 * (0.5 / 1250 )

= 0.03
At 96% confidence interval estimate of the population mean
is,

- E <   < + E

2.5 - 0.03 <   < 2.5+ 0.03

2.47 <   < 2.53

( 2.47 ,2.53 )