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 145 students in the high school and found a mean of 198 messages sent per day with a standard deviation of 59 messages. At the 95% confidence level, find the margin of error for the mean, rounding to the nearest whole number. (Do not write plus or minus±).

Answer 1

To find the margin of error for the mean number of text messages sent per day at a 95% confidence level, use the formula with a z-score of 1.96, and the given standard deviation and sample size. The margin of error is 10 messages after rounding to the nearest whole number.

Step-by-step explanation:

The student is asking about the margin of error for the mean number of text messages sent per day according to the study, at a 95% confidence level.

To calculate the margin of error (ME), we use the formula ME = z* (σ/√n), where z* is the z-score corresponding to the desired confidence level, σ is the standard deviation, and n is the sample size.

For a 95% confidence level, the z-score (z*) is typically 1.96. We have a standard deviation (σ) of 59 messages and a sample size (n) of 145.

Substituting the numbers into the formula yields ME = 1.96 * (59/√145).

Simplifying gives us the margin of error.

When you calculate this, you'll find the margin of error to be approximately 9.526, which when rounded to the nearest whole number, is 10 messages.