The following frequency distribution shows the monthly stock returns for Home Depot for the years 2003 through 2007. Over the time period, the following summary statistics are provided: Mean = 0.31%, Standard deviation = 6.49%, Skewness = 0.15, and Kurtosis = 0.38. At the 5% confidence level, which of the following is the correct conclusion for this goodness-of-fit test for normality?
A) Reject the null hypothesis; conclude that monthly stock returns are normally distributed with mean 0.31% and standard deviation 6.49%.
B) Reject the null hypothesis; conclude that monthly stock returns are not normally distributed with mean 0.31% and standard deviation 6.49%.
C) Do not reject the null hypothesis; conclude that monthly stock returns are normally distributed with mean 0.31% and standard deviation 6.49%
D) Do not reject the null hypothesis; conclude that monthly stock returns are not normally distributed with mean 0.31% and standard deviation 6.49%.

Question

The following frequency distribution shows the monthly stock returns for Home Depot for the years 2003 through 2007.  Over the time period, the following summary statistics are provided: Mean = 0.31%, Standard deviation = 6.49%, Skewness = 0.15, and Kurtosis = 0.38. At the 5% confidence level, which of the following is the correct conclusion for this goodness-of-fit test for normality?
A) Reject the null hypothesis; conclude that monthly stock returns are normally distributed with mean 0.31% and standard deviation 6.49%. 
B) Reject the null hypothesis; conclude that monthly stock returns are not normally distributed with mean 0.31% and standard deviation 6.49%. 
C) Do not reject the null hypothesis; conclude that monthly stock returns are normally distributed with mean 0.31% and standard deviation 6.49% 
D) Do not reject the null hypothesis; conclude that monthly stock returns are not normally distributed with mean 0.31% and standard deviation 6.49%.

Quizplus · Accepted Answer

Since the null hypothesis is that the data is normally distributed, we need to conduct a goodness-of-fit test for normality. The provided values for skewness and kurtosis are both relatively close to zero, which suggests that the data is approximately normally distributed. Additionally, since the p-value for the test is not provided, we cannot make a definitive conclusion to reject or fail to reject the null hypothesis. Therefore, the correct choice is to not reject the null hypothesis and conclude that the monthly stock returns for Home Depot are normally distributed with mean 0.31% and standard deviation 6.49%.

The Following Frequency Distribution Shows the Monthly Stock Returns for Home