Question

The nutrition label for Oriental Spice Sauce states that one package of sauce has 1010 milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 110 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1067.38 milligrams of sodium per package with a sample standard deviation of 274.89 milligrams.

Calculate a 95% confidence interval for the mean sodium content in Oriental Spice Sauce.

Answer #1

Solution :

Given that,

Point estimate = sample mean = = 1067.38 milligrams

sample standard deviation = s = 274.89 milligrams

sample size = n = 110

Degrees of freedom = df = n - 1 = 110 - 1 = 109

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2
= 0.025

t/2,df
= t_{0.025,109} = 1.982

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

= 1.982 * (274.89 / 110)

Margin of error = E = 51.95

The 95% confidence interval estimate of the population mean is,

± E

= 1067.38 ± 51.95

= ( 1015.43, 1119.33 )

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