Question

normally distributed with an unknown population mean and a population standard deviation of 4.5 points. A random sample of 45 scores is taken and gives a sample mean of 84. Find a 90% confidence interval

Answer 1

= ( 82.90, 85.10) points

Therefore at 90% confidence interval (a,b)= ( 82.90, 85.10) points

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 84

Standard deviation r = 4.5

Number of samples n = 45

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

84+/-1.645(4.5/√45)

84+/-1.645(0.670820393249)

84+/-1.10

= ( 82.90, 85.10) points

Therefore at 90% confidence interval (a,b)= ( 82.90, 85.10) points