Question

A random sample of 85 adults found that average calorie consumption was 2,100 per day. previous research has found a standard deviation of 450 calories, and you assume this value for . a researcher has been given $10,000 to conduct a similar survey, which costs $50.00 per person surveyed. she must compute a 95% confidence interval. given her budget restriction, what would the minimum margin of error be for the confidence interval for the population mean?

Answer 1

Average consumption, p = 2,100
Standard deviation assumed from previous studies, sd = 450
Z (at 95% confidence interval) = 1.96
Amount of funds available = $10,000
Cost per person supplied = $50.00

Therefore,
Sample size, n = 10000/50 = 200

Minimum margin of error will be achieved when the sample size is bigger than 85 adults.

Margin error = Z*sd/Sqrt (n) = 1.96*450/Sqrt (200) = +/- 62.37

Additionally,
Lowest range = 2100-62.37 = 2,037.63
Highest range = 2100+62.37 = 2,162.37