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?
|null hypothesis: Ho: σ =||110.000|
|Alternate hypothesis: Ha: σ >||110.000|
|for 10 % level and given df critical values of X2 =33.196|
|test statistic X2 =(n-1)s2/ σ2=||(25-1)*23971.121/12100=||47.5460|
since test statistic >critical value we reject null
we have sufficient evidence to conclude that variation exceeds the desired level
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