Question

The nutrition label for Oriental Spice Sauce states that one package of sauce has 1120 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 60 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1042.86 milligrams of sodium per package with a sample standard deviation of 249.05 milligrams.

Step 1 of 2 :  

Calculate a 90%90% confidence interval for the mean sodium content in Oriental Spice Sauce.

Answer 1

Solution :

Given that,

= 1042.86 milligrams

s = 249.05 milligrams.

n = 60

Degrees of freedom = df = n - 1 = 60 - 1 = 59

At 90% confidence level the t is ,

  = 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,59 = 1.671

Margin of error = E = t_/2,df * (s /n)

= 1.671 * (249.05/ 60 )

= 53.73

Margin of error = 53.73

The 90% confidence interval estimate of the population mean is,

- E < < + E

(1042.86 - 53.73 < < 1042.86 + 4:53.73)

989.13 < < 1096.59

(989.13 ,1096.59 )

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