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 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?

Answer 1

step 1:

null hypothesis:     Ho:   σ          =		110.000
Alternate hypothesis: Ha: σ   >		110.000

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=

47.5460

step 4:

since test statistic >critical value we reject null

step 5:

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