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 30 students in the high school and found a mean of 181 messages sent per day with a standard deviation of 70 messages. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest whole number. Margin of Error = 2(sn√)2(𝑠𝑛)where s is the standard deviation and n is the sample size.
Question
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 30 students in the high school and found a mean of 181 messages sent per day with a standard deviation of 70 messages. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest whole number. Margin of Error = 2(sn√)2(𝑠𝑛)where s is the standard deviation and n is the sample size.
Solution
To find the margin of error for the mean, we will use the formula provided:
Margin of Error = 2(s/√n)
where s is the standard deviation and n is the sample size.
Here, s = 70 (the standard deviation) and n = 30 (the sample size).
First, we need to calculate the denominator of the formula, which is the square root of n (√n).
√n = √30 = 5.48 (rounded to two decimal places)
Next, we divide the standard deviation (s) by the square root of n (√n).
s/√n = 70/5.48 = 12.77 (rounded to two decimal places)
Finally, we multiply this result by 2 to find the margin of error.
Margin of Error = 2 * 12.77 = 25.54
Rounding to the nearest whole number, the margin of error for the mean is 26.
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