A stock market analyst wants to estimate an average return...

A stock market analyst wants to estimate an average return on a certain stock. It is know that the Distribution of stock returns is Normal. Construct the following Confidence Intervals for an average return on this stock, based on the information provided in each question. 1) 95%: a random Sample of 15 days yields an average return of 10.37% and a Standard Deviation of 3.5%. 2) 90%: a random Sample of 20 days yields an average return of 12.5% and a Standard Deviation of 2.2%. 3) 99%: a random Sample of 10 days yields an average return of 10.75% and a Standard Deviation of 3.1% (Most likely need a t-test, not a z-test)

Transcript

00:01 So we want to find three confidence intervals, and our confidence intervals are going to be t intervals, because we don't know the population standard deviation, but we're assuming that the population is approximately normal.

00:15 So the first one is a 95%, and then the second one is a 90%, and the last one is a 99%.

00:23 And let me just give you some information here.

00:26 We have a sample size, we have an x bar, and we have a sample standard.

00:30 Standard deviation.

00:31 And so the sample sizes were 15, 20, and 10.

00:36 And the means were 10 .37, that's in percent, 12 .5 percent, 10 .75 percent.

00:46 And then our standard deviations were 3 .5, 2 .2, and 3 .1.

00:55 Now, i will show the calculation for each, and then i'm going to actually use on my calculator.

01:01 I'm going to use a t interval.

01:04 I have a t -i -84, and i'm going to enter in the statistics.

01:08 So i'm going to tell that my mean on that first one is 10 .37, and then i'm going to put the standard deviation in.

01:18 That's 3 .5.

01:19 My sample size is 15, and my confidence level is 0 .95.

01:23 So i will be taking 10 .37 plus or minus, and the t value that i use for 95 % is a 2 .145, and then i take my sample standard deviation divided by the square root of 15.

01:41 And i'm writing it down for you, but i'm going to use my calculator to actually calculate the interval...

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