Question

# The manufacturers of Oriental Spice Sauce are concerned that the sodium levels in their product vary...

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?

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.