A study of a local high school tried to determine the mean number of text messages that each student sent per day. The study surveyed a random sample of 128 students in the high school and found a mean of 197 messages sent per day with a standard deviation of 88 messages. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write ±）

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maheshpatelvVT maheshpatelvVT · Answer 1 · 2022-06-02T13:02:54+02:00

The margin of error for the mean is 15% if rounding to the nearest whole number.

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where Z is the z-score at the confidence interval

s is the standard deviation

n is the number of samples.

Z score at the 95% confidence level = 1.959

s = 88

n = 128

[tex]\rm MOE = 1.959\times \dfrac{88}{\sqrt{128}}[/tex]

MOE = 15.244 ≈ 15%

Thus, the margin of error for the mean is 15% if rounding to the nearest whole number.

Learn more about the Margin of error here:

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