Question
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.
. 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.
Answers
GPT 3.5
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.
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.