Question

1. The mean salt content of a certain type of potato chip is supposed to be 2.0 mg. From each batch produced, the inspector takes an SRS of 50 bags, notes there are no outliers, and measures the salt content and gets a mean of 2.05 mg with a standard deviation 0.1. Construct and interpret a 95% confidence interval for the mean salt content of all such bags. Is there a problem with the potato chip manufacturing? (6 points)
2. After calculating a confidence interval you decide the error is too high. Name two things you can do to lower the error on your interval. (2 points)
3. Dr Coon wants you to estimate the mean number of hours students enrolled in Math 115 spend on homework with 99% confidence. How many students will you need to survey to estimate the number of hours within an error of no more than 20 minutes? It's known from previous research that the standard deviation for the number of hours studied per week is 2 hours. (2 points)

Answer 1

Here sample size is large enough so we can use z distribution as per central limit theorem

z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is

Hence CI is

So population mean will lie in the range of 2.022 to 2.078

As 2 is not in the range there is problem with the potato chip manufacturing

To reduce the error we need to increase the sample size and reduce the CI level as doing both of this will reduce the margin of error

For Dr. Coon it is given that Margin of Error is 20/60

For 99% CI, z value is 2.58 as P(-2.58<z<2.58)=0.99

Also given is sd=2

So we will find n using formula of E