Confidence Interval for µ question

Question

Sixty-four randomly selected adults who buy books for general reading were asked how much they usually spend on books per year. The sample produced a mean of $1450 and a standard deviation of $300 for such annual expenses. Determine a 99% confidence interval for the corresponding population mean.

 

Can you explain to me if σ(sigma) is known or unknown? Thanks

Answer 1

In general when sigma is not known and the sample is of moderate size (> 30) using the z-distribution is appropriate by using s in place of sigma.

 

However it is NOT incorrect to use the t-distribution when sigma is unknown. In this case degrees of freedom would be 63.

 

If you compare the t-score with the z-score you will see they are very close together. The greater the value of n the closer the scores will be.

 

As to which way to do it you have to rely on your text and/or the techniques your teacher wants to see.

Answer 2

sigma denotes the standard deviation. the standard deviation is given in this problem.