Questions: Colonial Funds claims to have a bond fund which has maintained a mean share price of 14.00. They claim that the standard deviation of the share price is 0.19. To test this claim, the investor randomly selects 12 days during the last year. He finds an average share price of 13.80 with a standard deviation of 0.1302. Can the investor conclude that the share price of the bond fund varies from Colonial Funds claims at α=0.05? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. Answer H0: Ha:

Colonial Funds claims to have a bond fund which has maintained a mean share price of 14.00. They claim that the standard deviation of the share price is 0.19. To test this claim, the investor randomly selects 12 days during the last year. He finds an average share price of 13.80 with a standard deviation of 0.1302. Can the investor conclude that the share price of the bond fund varies from Colonial Funds claims at α=0.05? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. Answer H0: Ha:
Transcript text: Colonial Funds claims to have a bond fund which has maintained a mean share price of $\$ 14.00$. They claim that the standard deviation of the share price is 0.19 . To test this claim, the investor randomly selects 12 days during the last year. He finds an average share price of $\$ 13.80$ with a standard deviation of 0.1302 . Can the investor conclude that the share price of the bond fund varies from Colonial Funds claims at $\alpha=0.05$ ? Step 1 of 5 : State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. Answer Tables Keypad Keyboard Shortcuts \[ \begin{array}{l} H_{0}: \square \\ H_{a}: \square \end{array} \]
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Solution

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Solution Steps

Step 1: State the Hypotheses
  • $H_0: \sigma^2 = 0.0361$
  • $H_1: \sigma^2 \neq 0.0361$
Step 2: Calculate the Test Statistic
  • Using the chi-square test: $\chi^2 = \frac{(n-1)s^2}{\sigma^2_0} = 5.165$
Step 3: Determine the Critical Value(s)
  • Critical value(s): 3.816 and 21.92

Final Answer:

  • Fail to reject $H_0$. The sample does not provide enough evidence to support the claim.
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