Question

Dwight Schrute is interested in the weight of a single sheet of paper. He measures 15 pieces of paper and finds the sample standard deviation to be 0.0083 grams. He would like to test whether or not the standard deviation differs from 0.01 grams. Use a=0.05. What is the 95% confidence interval?

Answer 1

Solution:

Given:

Sample size = n = 15

Sample standard Deviation = s = 0.0083

Part a) We have to test whether or not the standard deviation differs from 0.01 grams.

Level of significance =a = 0.05

Step 1) State H0 and H1:

Vs

Step 2) Find test statistic:

Step 3) Find Chi-square critical values:

Since this is two tailed test, find a/ 2 = 0.05 / 2 = 0.025 and 1 - a/2 = 1 - 0.025 = 0.975

df = n- 1 = 15 -1 = 14

Look in Chi-square table for df = 14 and two areas 0.025 and 0.975

Thus and

Step 4) Decision Rule:

Reject H0 , if Chi-square test statistic value < or > , otherwise we fail to reject H0.

Since Chi-square test statistic value = is neither < nor > , we fail to reject H0.

Step 5) Conclusion:

The standard deviation does not differs from 0.01 grams.

Part b) What is the 95% confidence interval?

Formula: