Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 5%. A mutual-fund rating agency randomly selects 24 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 4.54%. Is there sufficient evidence to conclude that the fund has moderate risk at the α=0.05 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed. What are the correct hypotheses for this test? The null hypothesis is H0

Question

contestada

Respuesta :

fichoh fichoh · Answer 1 · 2021-07-27T03:28:03+02:00

Answer:

H0 : σ = 5

H1 : σ < 5

there is no sufficient evidence to conclude that fund has moderate risk.

Explanation:

The hypothesis :

H0 : σ = 5

H1 : σ < 5

The test statistic using the Chisquare variance test :

χ² = (n-1)*s²/σ²

The sample size, s = 4.54

The sample size, n = 24

α = 0.05

Test statistic ;

χ² = [(24 - 1) * 4.54²] / 5²

χ² = (23 * 20.6116) / 25

χ² = 18.962

The Pvalue :

df = n - 1 = 24 - 1 = 23

Pvalue(0.05, 23) = 0.7034

Since Pvalue > α ; we fail to reject the Null ;

Hence, there is no sufficient evidence to conclude that fund has moderate risk.