Question

The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 27 text messages is taken and results in a sample mean of 29 characters, find a 95% confidence interval for the population mean. Round your answers to two decimal places.

Answer 1

29+/-2.26

= (26.74, 31.26) characters

Therefore the 95% confidence interval (a,b) = (26.74, 31.26) characters

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 = 29 characters

Standard deviation r = 6 characters

Number of samples n = 27

Confidence level = 95%

z value(at 95% confidence) = 1.96

Substituting the values we have;

29+/-1.96(6/√27)

29+/-1.96(1.154700538379)

29+/-2.263213055223

29+/-2.26

= (26.74, 31.26) characters

Therefore the 95% confidence interval (a,b) = (26.74, 31.26) characters