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I am having trouble


I am working on a problem here. It is a sample of 9 bonds taken from a normally distributed population. The population has a mean of 16% and a variance of 144. If a bond is selected at random, a 90% confidence interval for its return is:

My thought here was that i’d use the t-table (also tried Z to be clear) using the df to get the t-stat(or z) and multiply by the standard error i calculated as the Std Dev of 12/ sqrt9 and then +/- this value from the mean to get a range for the confidence interval. But doing this seems to not get me anywhere. 

I’m worried I am simply doing this all wrong and im not catching on. Any guidance is appreciated.

(the correct answer on this according to my book is -3.74% to 35.74%)

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(-3.74%, 35.74%) is the 90% confidence interval for the population mean = 16 +/- 1.645 * 12. Did the question wording say just “the return”?

“Mmmmmm, something…” - H. Simpson

It did. But why does that mean we multiply the Z score by the standard deviation and not the standard error? Sorry if that’s an elementary question. 

“If a bond is selected at random…”:  you are picking only one bond out of the sample of 9.  They tell you the population is normally distributed, so you use the z curve.

“Mmmmmm, something…” - H. Simpson

I think im still missing why standard error isn’t used. How would this question be worded to indicate the use of standard error rather than standard deviation alone?

Thank you for the guidance, kind stranger.