The following table shows the observed frequencies of the quarterly returns for a sample of 60 hedge funds. The table also contains the hypothesized proportions of each class assuming the quarterly returns have a normal distribution. The sample mean and standard deviation are 3.6% and 7.4% respectively.ClassObservedExpected piReturn < ?5140.122?5 ? Return < 0110.1910 ? Return < 5100.2625 ? Return < 10110.231Return ? 10140.194a. Set up the competing hypotheses for the goodness-of-fit test of normality for the quarterly returns.b. Calculate the value of the test statistic and determine the degrees of freedom.c. Compute the p-value. Does the evidence suggest that the quarterly returns do not have a normal distribution at the 10% significance level?
What will be an ideal response?
a. H0: Quarterly returns follow a normal distribution with mean 3.36% and standard deviation 7.4%; HA: Quarterly returns do not follow a normal distribution with mean 3.36% and standard deviation 7.4%
b. 9.26 and the degrees of freedom are 2.
c. The p-value is less than 0.01. Because the p-value is less than the significance level, reject the null hypothesis. Conclude the quarterly returns do not have a normal distribution.
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