Question

A random sample of size 36 has sample mean 12 and sample standard deviation 3. (a) Check Requirements: Is it appropriate to use a Student’s t distribution to compute a confidence interval for the population mean ? Explain. (b) Find a 80% confidence interval for µ. [round E to 2 d.p.] (c) Interpretation: Explain the meaning of the confidence interval you computed.

Answer 1

Solution:

a. The requirements are:

The sample drawn from the population is random. In the given question, this condition is satisfied as a random sample is drawn from the population.

The population should be approximately normally distributed. In the given question, the sample size is large enough (>30) to consider the data has come from a normally distributed population.

b. The 80% confidence interval is:

Where:

is the critical value at 0.20 significance level for degrees of freedom 35

Therefore, the confidence interval is:

c. There is an 80% chance that the confidence interval calculated contains the true value of the population mean