Question

Suppose that the lengths, in inches, of adult corn snakes are normally distributed with an unknown mean and standard deviation. A random sample of 38 snakes is taken and gives a sample mean of 51 inches and a sample standard deviation of 8 inches.

The margin of error, for a 95% confidence interval estimate for the population mean using the Student's t-distribution is determined to be 2.63.

Find a 95% confidence interval estimate for the population means using the Student's t-distribution.

• Round the final answers to two decimal places.

Provide your answer below:

We are 95% confident that the true population mean lies between ____ and ____?

Answer 1

Solution :

Given that,

t /2,df = 2.026

Margin of error = E = t/2,df * (s /n)

= 2.026 * (8 / 38)

Margin of error = E = 2.63

The 95% confidence interval estimate of the population mean is,

- E < < + E

51 - 2.63 < < 51 + 2.63

48.37 < < 53.63

95% confident that the true population mean lies between 48.37 and 53.63