Question

Use R built-in functions covered in this course to solve the question below. The following data represent the 10-year rate of return from a random sample of 10 ETF funds. Construct and interpret the 95% confidence interval for the mean rate of return, whichever is appropriate. The dataset below is listed as an R command format so that you may copy it and paste in R. ETF=c(16.15,31.76,33.37,17.60,25.49,10.73,33.09,26.35,27.32,28.53) Assume the data is taken from an approximately normal population. The population standard deviation is known to be 8.

Answer 1

To construct a confidence interval for the mean rate of return, calculate the point estimate for the population mean (sample mean), calculate the error bound using the z-value, and construct the confidence interval using the formulas.

Step-by-step explanation:

To construct a confidence interval for the mean rate of return, we can use R built-in functions. Since the population standard deviation is known, we can use the z-distribution. First, we calculate the point estimate for the population mean, which is the sample mean. Next, we calculate the error bound using the formula: EBM = (z-value) * (population standard deviation) / sqrt(sample size). Finally, we construct the confidence interval using the formula: (point estimate - error bound, point estimate + error bound).

For the given dataset, the point estimate for the population mean is the sample mean. The sample mean is calculated by summing all the ETF values and dividing it by the sample size, which is 10 in this case. The error bound can be calculated using the formula with the z-value corresponding to a 95% confidence level. The confidence interval can then be constructed using the formula mentioned above.