To calculate the minimum sample size needed, we can use the formula for sample size in a confidence interval, which is:
n = ((Z * σ) / E)^2
Where:
n = sample size
Z = Z-value for desired confidence level (80% confidence corresponds to Z = 1.28)
σ = standard deviation of the population
E = maximum error allowed in the confidence interval
Plugging in the values given:
Z = 1.28
σ = 0.6
E = 0.06
n = ((1.28 * 0.6) / 0.06)^2
n = (0.768 / 0.06)^2
n = 12.8^2
n = 163.84
Since we must round up to the next integer, the minimum number of people over age 23 that they must include in their sample is 164.
A research company desires to know the mean consumption of meat per week among people over age 23
. They believe that the meat consumption has a mean of 4.6
pounds, and want to construct a 80%
confidence interval with a maximum error of 0.06
pounds. Assuming a standard deviation of 0.6
pounds, what is the minimum number of people over age 23
they must include in their sample? Round your answer up to the next integer.
1 answer
1 answer