Question

The nutrition label for Oriental Spice Sauce states that one package of sauce has 1080

milligrams of sodium. To determine if the label is accurate, the FDA randomly selects 120
packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1154.13
milligrams of sodium per package with a sample standard deviation of 242.02
milligrams.
Step 1 of 2 : Calculate a 90%
confidence interval for the mean sodium content in Oriental Spice Sauce. Round your answers to two decimal places.

Answer 1

The 90% confidence interval for the mean sodium content of Oriental Spice Sauce is approximately (1117.56 mg, 1190.70 mg) based on the provided sample data and calculations.

Step-by-step explanation:

To calculate a 90% confidence interval for the mean sodium content in Oriental Spice Sauce using a sample mean of 1154.13 mg, a sample standard deviation of 242.02 mg, and a sample size of 120 packages, we can use the t-distribution since the population standard deviation is unknown.

First, we find the critical value (tα/2) for a 90% confidence interval with 119 degrees of freedom (n-1). Using a t-distribution table or calculator, we get approximately 1.656 for the critical value.

Now we compute the standard error (SE) of the mean: SE = s / √n, where 's' is the sample standard deviation and 'n' is the sample size. SE = 242.02 / √120 ≈ 22.09 mg.

Next, we calculate the margin of error (ME): ME = tα/2 × SE ≈ 1.656 × 22.09 ≈ 36.57 mg.

Finally, we find the confidence interval by adding and subtracting the margin of error from the sample mean:

Lower limit = 1154.13 - 36.57 ≈ 1117.56 mg, Upper limit = 1154.13 + 36.57 ≈ 1190.70 mg.

Therefore, the 90% confidence interval for the true mean sodium content per package of Oriental Spice Sauce is approximately (1117.56 mg, 1190.70 mg).