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Orlov [11]
3 years ago
6

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 pe

rson 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
Mathematics
1 answer:
NNADVOKAT [17]3 years ago
7 0

Answer:

{13.7756,18.2244}

Step-by-step explanation:

Given the sample size, the margin of error can be calculated with the formula M=Z*\frac{\sigma}{\sqrt{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*\frac{\sigma}{\sqrt{n}}=1.645*(\frac{8}{\sqrt{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}

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