Question

The manufacturers of Oriental Spice Sauce are concerned that the sodium levels in their product vary too much. A package of the sauce is supposed to contain 700mg of sodium with a standard deviation of 140mg. A sample of 20 packages was analyzed and the sample standard deviation was 240.0092mg. 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.

Step 5 of 5: What is the conclusion?

Answer 1

1)

H0: = 140

HA: > 140

2)

This is right tailed test

Critical value at 0.01 level with 19 df = 36.191

3)

Test statistics

= ( n - 1) * S2 / 2

= 19 * 240.00922 / 1402

= 55.84

4)

Decision = Since test statistics > 36.191, Reject H0.

5)

Conclusion =

We have sufficient evidence to support the claim that he standard deviation of the sodium content

exceeds the desired level.