Final answer:
The 99% confidence interval for the mean sodium content in Oriental Spice Sauce is calculated to be between 1016.22 mg and 1163.06 mg per package.
Step-by-step explanation:
To calculate a 99% confidence interval for the mean sodium content in Oriental Spice Sauce, we will use the following information: the sample mean (Öx) is 1089.64 milligrams, the sample standard deviation (s) is 248.67 milligrams, and the sample size (n) is 80. We use the t-distribution because the population standard deviation is unknown.
First, we find the t-value that corresponds to a 99% confidence level and a sample size of 80, which gives us degrees of freedom (df) equal to 79. Using a t-distribution table or software, we find the t-value for a two-tailed test at the 99% confidence level and df=79 is approximately 2.64.
Next, we calculate the standard error of the mean (SEM) using the sample standard deviation divided by the square root of the sample size:
SEM = s / √n
SEM = 248.67 / √80
SEM = 27.81
Now, we can calculate the margin of error (ME) using the t-value and SEM:
ME = t-value × SEM
ME = 2.64 × 27.81
ME = 73.42
Finally, the 99% confidence interval is calculated by subtracting and adding the margin of error from the sample mean:
Lower limit = Öx - ME
= 1089.64 - 73.42
= 1016.22 mg
Upper limit = Öx + ME
= 1089.64 + 73.42
= 1163.06 mg
The 99% confidence interval for the mean sodium content per package of Oriental Spice Sauce is 1016.22 mg to 1163.06 mg.