Question

An investor wants to invest his money in a fund that has maintained a steady value. A fund manager claims that one of his bond funds has maintained an average price of $18.00 with a variance of 0.1. In order to find out if the fund manager's claim is true, the investor samples the prices from 15 random days and finds a standard deviation of 0.2813 in the price. Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α=0.05? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision. (Reject or Fail to reject the Null)

Step 5 of 5: What is the conclusion? (Sufficient of insufficient evidence)

Answer 1

Given,

: Variance of Bond funds

variance of the share price of the bond fund is different than 0.1 i.e 0.1

Step 1 of 5:

null and alternative hypotheses

Null hypothesis : Ho : = 0.1

Alternative Hypothesis : H1 :   0.1

Two tailed test:

Step 2 of 5: critical value(s) of the test statistic.

Two tailed test:

α=0.05; sample size : n= 15

Degrees of freedom =n-1 =15-1=14

Critical values :

Critical values : (5.6287,26.1189)

Step 3 of 5: Determine the value of the test statistic.

Hypothesize Variance : =0.1

Sample size : Number of days randomy sampled : n=15

Sample standard deviation : s=0.2813

Test Statistic = 11.078

Step 4 of 5: Make the decision

As Value of the test statistic is within the Critical Values i.e.( 5.6287 < 11.0782 < 26.1189 )Fail To Reject Null Hypothesis
Fail to reject the null hypothesis.

Step 5 of 5: What is the conclusion? (Sufficient of insufficient evidence)

There is insufficient evidence to conclude that the variance of the share price of the bond fund is different than claimed