The correct hypotheses for this test are:
Null hypothesis (H0): The standard deviation of the mutual fund's monthly rate of return is greater than or equal to 3%.
Alternative hypothesis (H1): The standard deviation of the mutual fund's monthly rate of return is less than 3%.
To determine if there is sufficient evidence to reject the null hypothesis and conclude that the fund has moderate risk, you would need to perform a hypothesis test. In this case, since you have a sample of 27 monthly rates of return and the normal probability plot indicates that the data is normally distributed, you can use a z-test for the population standard deviation.
To perform the test, you would need to calculate the test statistic and the p-value. The test statistic is calculated as follows:
test statistic = (sample standard deviation - population standard deviation) / (standard error)
where the sample standard deviation is 2.55%, the population standard deviation is 3%, and the standard error is calculated as:
standard error = sample standard deviation / sqrt(sample size)
Plugging in the values, the test statistic is:
test statistic = (2.55 - 3) / (2.55 / sqrt(27)) = -0.44
The p-value is the probability of observing a test statistic at least as extreme as the one calculated, given that the null hypothesis is true. To calculate the p-value, you can use a z-table or a statistical software package.
If the p-value is less than the chosen level of significance (a=0.05 in this case), you can reject the null hypothesis and conclude that the fund has moderate risk. If the p-value is greater than the level of significance, you cannot reject the null hypothesis and cannot conclude that the fund has moderate risk.