Question

find the margin of error to use for this sample mean sushi based on a sample of 35 people he average out of pieces of sushi a person can eat is 16 pieces with a standard deviation of 8 pieces of sushi .constructs 90% confidence interval for the mean of amount of sushi pieces a person can eat statistics

Answer 1

{13.7756,18.2244}

Explanation:

Given the sample size, the margin of error can be calculated with the formula
`M=Z*(\sigma)/(√(n))` where Z is the critical value for the desired confidence level, σ is the population standard deviation, and n is the sample size. Therefore, our margin of error for a 90% confidence level is:

`M=Z*(\sigma)/(√(n))=1.645*((8)/(√(35)))=2.2244`

The formula for a confidence interval is
`CI=\bar{x}+M` where x-bar is the sample mean. Therefore, the 90% confidence interval for the mean amount of sushi pieces a person can eat is:

`CI=\bar{x}\pm[M]=16\pm2.2244={13.7756,18.2244}`

Therefore, we are 90% confident that the true mean amount of sushi pieces a person can eat is contained within the interval {13.7756,18.2244}