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)s^{2}/ σ^{2}= |
(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

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