Question

In order to ensure the consistency of their product, the Oriental Spice Sauce company has a strict policy that the standard deviation of the sodium content in the product is 120mg . For one size of bottle, the sodium content is supposed to be 900mg . In a random sample of 23 bottles, the standard deviation was found to be 183.4773mg . 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.

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.

Step 5 of 5:

what is the conclusion?

                                     

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: Hypotheses:

H₀ : σ < 120
H_A : σ > 120

Step - 2: Critical value = 36.781

Step - 3: Test statistic = 51.431

Step - 4: Decision: Reject the null

Step - 5: We have sufficient evidence to conclude that the standard deviation of the sodium content exceeds the desired level