Question

Calculate the 95% confidence intervals for the four different investments included in the following table. Small shares 20.14% 41.17% Average annual return (%) Standard deviation of returns (%) Large shares 11.42% 19.93% Corporate bonds 6.77% Treasury notes 3.06% 4.65% 7.47% The 95% confidence interval of small shares is between % and %. (Enter your response as a percent rounded to two decimal places and put the lower number first.) The 95% confidence interval of large shares is between % and %. (Enter your response as a percent rounded to two decimal places and put the lower number first.) The 95% confidence interval of corporate bonds is between % and %. (Enter your response as a percent rounded to two decimal places and put the lower number first.) The 95% confidence interval of Treasury notes is between % and %. (Enter your response as a percent rounded to two decimal places and put the lower number first.)

Answer 1

The 95% confidence interval of small shares is between 12.07% and 28.21%.

The 95% confidence interval of large shares is between 7.51% and 15.33%.

The 95% confidence interval of corporate bonds shares is between 5.31% and 8.23%.

The 95% confidence interval of treasury notes is between 2.15% and 3.97%.

Please refer to attached image for calculations.

Confidence Interval formula CI= a + 2 a where n is the sample mean. z the the represents the zt-value from standard normal distribution desired confidence livel. for n o is is the the sample population size standard duration is not given, we assume since, sample size n = 106. for 95% confidence internal, z = 1.96 for small shares, ū - 20.14%, s = 41.17% CI = 20.14% ± 1.96 x 41.177. = 112.07% 28.21%. Similarly, for lange shares I = 11.42 7. I 1.96€ 19.93% = (7.514., 15.33%) 10 for corporate bonds, CI = 6.777. I 1.96 x 7.47% = (5.31% 8.231) for Treasury notes 10 (I = 3.06%. £ 1.96x4.657 = (2.15%3.971) - - -