Question

00:57:14 Question1- of 9 Step 4 of 5 An investor wants to invest his money in a fund which has maintained a steady value. A fund manager claims that one of his bond funds has maintained an e of $7,00 with a variance of 0.2. in order to find out if the fund manager's claim is true, the investor samples the prices he investor conclude that the variance of the share price of the from 13 random days and finds a standard devistion of 0.2475 in the price. Can t bond fund is different than claimed at a0.17 Assume the population is normally distributed Step 4 of S: Make the decision Keypad Answer 1 Point Reject Null Hypothes O Fail to Reject Null Hypothesis Next Prev

Answer 1

Let $\sigma^2$ denote the variance of the share price bond.

To test $H_0:\sigma^2 =0.2$ against $H_1:\sigma^2 \neq 0.2$

The test statistic can be written as

$\chi^2 = \frac{(n-1)s^2}{0.2}$ which under H₀ follows a $\chi^2$ distribution with df.

We reject H₀ at 10% level of signficance if $\chi^2_{obs} > \chi^2_{0.05,n-1}$

Here

The value of the test statistic $\chi^2_{obs} = 3.67537$

and critical value $\chi^2_{0.05,12} = 21.0261$

Since $\chi^2_{obs} = 3.67537 \ngtr \chi^2_{0.05,12} = 21.0261$ , we fail to reject H₀ at 10% level of signficance and we can conclude that the variance of the share price bond is not significantly different from the value that is claimed.