Question

From Jan. 1, 1960 to Jan. 1, 1985, the historical average annual rate of return in the hypothetical country of Westeros was 12%. The annual standard deviation of the rate of return is 10%. What is the upper bound of the 95.4% confidence interval for the annual rate of return based on this information?

Answer 1

What is the upper bound of the 95.4% confidence interval for the annual rate of return based on this information?

34%

Explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

`\bar X=12` represent the sample mean for the sample

`\mu` population mean (variable of interest)

`\sigma=10` represent the population standard deviation

2) Confidence interval

The confidence interval for the variable of interest, is given by the following formula:

`\bar X \pm z_(\alpha/2)\sigma` (1)

Since the Confidence is 0.954 or 95.4%, the value of
`\alpha=0.046` and
`\alpha/2 =0.023`, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.023,10,1)".And we see that
`z_(\alpha/2)=2.00`

Now we have everything in order to replace into formula (1):

`12-2.00(10)=-10`

`12+2.00(10)=34`

So on this case the 99% confidence interval would be given by (-10%;34%) since the lower bound not have practical interpretation we are just interested on the upper bound.

What is the upper bound of the 95.4% confidence interval for the annual rate of return based on this information?

34%