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The nutrition label for Oriental Spice Sauce states that one package of sauce has 1110 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 170 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1172.61 milligrams of sodium per package with a sample standard deviation of 241.88 milligrams. Step 2 of 2 : Using the confidence interval approach, is there evidence that the sodium content is different from what the nutrition label states

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Answer:

[tex]1124.28 \text { to } 1220.94[/tex]

Step-by-step explanation:

A 99% confidence interval for the mean sodium content in Oriental Spice Sauce is,

First, compute t -critical value then find confidence interval.

The t critical value is,

The sample size is small and two-tailed test. Look in the column headed [tex]\alpha=0.01[/tex] and the row headed in the t distribution table by using degree of freedom is,

 d . f . =n-1

=170-1  

=169

The t critical value is 2.605 .

[tex]99 \% \text { C.I. } &=\bar{x} \pm t_{c} \times s / \sqrt{n}[/tex]

[tex]=1172.61 \pm 2.605 \times 241.88 / \sqrt{170}[/tex]

[tex]=1172.61 \pm 48.33[/tex]

[tex]=1124.28 \text { to } 1220.94[/tex]

A [tex]99%[/tex]confidence interval for the mean sodium content in Oriental Spice Sauce is  

[tex]1124.28 \text { to } 1220.94[/tex]

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