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 1100mg of sodium with a standard deviation of 110mg. A sample of 25 packages was analyzed and the sample mean was 1080mg and the sample standard deviation was 154.8261mg. Is there evidence at α=0.1 that variation exceeds the desired level?

Step 1 of 5 :

State the hypotheses in terms of the standard deviation. Round the standard deviation 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 test statistic.

Step 4 of 5:

Determine if whether to reject or fail the null hypothesis

Step 5 of 5:

What is the conclusion?

step 1:

 null hypothesis:     Ho:   σ          = 110 Alternate hypothesis: Ha: σ   > 110

step 2:

 for 10 % level and given df critical values of X2 =33.196

step 3:

 test statistic X2 =(n-1)s2/ σ2= (25-1)*23971.121/12100= 47.546

step 4:

since test statistic >critical value we reject null

step 5:

we have sufficient evidence to conclude that variation exceeds the desired level

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