Question

Milk is a good source of many vitamins that can help us stay healthy. FDA recommends that the average vitamin A concentration for whole milk should be 200.9220 micrograms per liter. A first study in 2016 collected a sample of 34 whole milk bottles and found the average vitamin A concentration was 207.9068 micrograms per liter with a standard deviation of 11.8841 micrograms per liter. A medical researcher wants to use this information to determine the sample size required to estimate the mean vitamin A concentration in whole milk at 95% confidence with a margin of error of no more than 0.3656 using the following formula, n = (t*sME)2. Note: Numbers are randomized for each instance of this question. Use the numbers given above. What is the degrees of freedom used to calculate the t* multiplier for this scenario?

Answer 1

Answer:

The degrees of freedom for this sample are 27.

The sample size to get a margin of error equal or less than 0.3656 is n=4450.

Step-by-step explanation:

The degrees of freedom for calculating the value of t are:

$df=n-1=28-1=27$

With 27 degrees of freedom and 95% confidence level, from a table we can get that the t-value is t=2.052.

The sample size to get a margin of error equal or less than 0.3656 can be calculated as:

$MOE=t\cdot s/\sqrt{n}\\\\n=\left(\dfrac{t\cdot s}{MOE}\right)^2=\left(\dfrac{2.052\cdot 11.8841}{0.3656}\right)^2=66.7^2\\\\\\n=4449.13\approx4450$