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 140mg. For one size of bottle, the sodium content is supposed to be 900mg. In a random sample of 11 bottles, the standard deviation was found to be 275.4444mg. Is there evidence at α=0.01 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.

Reject Null Hypothesis

Fail to Reject Null Hypothesis

Step 5 of 5:

What is the conclusion?

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

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

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis: σ = 140
Alternative Hypothesis: σ > 140

b)
Rejection Region
This is right tailed test, for α = 0.05 and df = 10
Critical value of ꭓ^2 is 18.307
Hence reject H0 if ꭓ^2 < 18.307

c)
Test statistic,
ꭓ^2 = (n-1)*s^2/σ^2
ꭓ^2 = (11 - 1)*275.4444^2/140^2
ꭓ^2 = 38.709

d)
Reject Null hypothesis

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