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 99 students in the high school and found a mean of 180 messages sent per day with a standard deviation of 63 messages. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write \pm±).
To find the margin of error for the mean at a certain confidence level, you can use the formula:
Margin of Error = Critical value * Standard deviation / Square root of sample size
In this case, the critical value will be based on the desired confidence level, which is 95%. Since the sample size is 99, we can calculate the margin of error.
1. Find the critical value:
To find the critical value for a 95% confidence level, you can use a z-table or a calculator with the standard normal distribution. For a 95% confidence level, the critical value is approximately 1.96.
2. Calculate the margin of error:
Margin of Error = 1.96 * Standard deviation / Square root of sample size
= 1.96 * 63 / sqrt(99)
≈ 13.72
Rounding to the nearest whole number, the margin of error is approximately 14.
Therefore, the margin of error for the mean number of text messages sent per day is approximately 14.