Question

We take a random sample of 16 scores from a

Math

Exam and the sample

mean is 80 (the population scores are normally distributed)

. The known

standard deviation = 16. What is the value of Lower Confidence Limit

at

90% CI.

Answer 1

SOLUTION:

From given data,

We take a random sample of 16 scores from a Math Exam and the sample mean is 80 (the population scores are normally distributed) . The known standard deviation = 16. What is the value of Lower Confidence Limit at 90% CI.

Where,

sample = n = 16

sample mean = = 80

standard deviation = =16

Confidence interval is 90%

90% = 90/100 = 0.90

= 1 - Confidence interval = 1-0.90 = 0.10

/2 = 0.10 / 2

= 0.05

Z_/2 = Z_0.05 = 1.645

The Lower Confidence Limit is

Lower Confidence Limit = -  Z_/2 * ( / )

= 80 - 1.645 * (16 / √16 )

= 80 - 1.645 * (16 / 4)

= 80 - 1.645 * 4

= 80 - 6.58

= 73.42

The value of Lower Confidence Limit at 90% CI is   73.42