Question

30. In an effort to make a healthier product, the Oriental Spice Sauce company has reduced the amount of sodium in their product to 800mg. In addition, the standard deviation of the amount of sodium should be 80. To make sure this new product continues to meet the standard, a random sample of 24 bottles is taken, and the standard deviation for the sample was 120.7812. Is there evidence at α=0.025 that the standard deviation of the sodium content exceeds the desired level? Assume the population is normally distributed.

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

H0:

Ha:

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.

A. Reject Null Hypothesis

B. Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion?

A. There is sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

B. There is not sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

Answer 1

Solution:
   We are given that: the standard deviation of the amount of sodium should be 80.

That is:

a random sample of 24 bottles is taken, and the standard deviation for the sample was 120.7812.

Sample size = n = 24

Sample standard deviation = s = 120.7812

We have to test of there is evidence at α=0.025 that the standard deviation of the sodium content exceeds the desired level.

Step 1: State the null and alternative hypotheses.

         Vs  

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

This is right tailed test, look in Chi-square table for df = n -1 = 24 - 1 = 23

Level of significance =

Chi square critical value =

So we have one critical value =

Step 3: Determine the value of the test statistic.

Step 4: Make the decision.

Since Chi-square test statistic value = > , we reject H0.

Thus correct option: A. Reject Null Hypothesis

Step 5) What is the conclusion?

Since we have rejected H0, we conclude that:

A. There is sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.