Canadians are becoming more conscious of the importance of good nutrition, and some researchers believe that we may be altering our diets to include less red meat and more fruits and vegetables. To test this theory, a researcher decides to select hospital nutritional records for subjects surveyed 10 years ago and to compare the average amount of beef consumed per year to the amounts consumed by an equal number of subjects she will interview this year. She knows that the amount of beef consumed annually by Canadians ranges from 0 to approximately 45 kg. How many subjects should the researcher select for each group if she wishes to estimate the difference in the average annual per-capita beef consumption correct to within 2.1 kg with 99% confidence?
Hello, can anyone explain to me how to do this please? Thank you!
yup
To estimate the required sample size, we can use the formula for sample size calculation in hypothesis testing:
n = (Z * σ / E)^2
Where:
n = Sample size
Z = Z-value for the desired confidence level (in this case, 99% confidence corresponds to a Z-value of 2.576)
σ = Standard deviation of the population (unknown in this case, so we'll estimate it as the range of beef consumption divided by 4)
E = Maximum desired margin of error (2.1 kg)
First, let's calculate the estimated standard deviation (σ):
Range of beef consumption = 45 kg (maximum) - 0 kg (minimum) = 45 kg
Estimated standard deviation (σ) = (Range of beef consumption) / 4 = 45 kg / 4 = 11.25 kg
Now, let's substitute the values into the formula and solve for the sample size (n):
n = (2.576 * 11.25 kg / 2.1 kg)^2
n = (28.98)^2
n ≈ 840 subjects per group
Therefore, the researcher should select approximately 840 subjects for each group to estimate the difference in average annual per-capita beef consumption with a 99% confidence level and a margin of error of 2.1 kg.