Question

1. A sample of 250 high-school students in a city results in an average number of text messages sent per month of 172.6, with a margin of error of + 4.8. If there are 3000 high-school students in the city, what is the estimated number of text messages sent in a month? between______ and____text messages ​

Answer 1

Explanation:

1) Find the upper bound of the confidence interval:

Upper bound = sample mean + margin of error

= 172.6 + 4.8

= 177.4

2) Find the lower bound of the confidence interval:

Lower bound = sample mean - margin of error

= 172.6 - 4.8

= 167.8

3) Estimate the total number of text messages sent in a month:

Total number of text messages sent = (number of students in the population / number of students in the sample) x sample mean

= (3000 / 250) x 172.6

= 2071.2

Therefore, the estimated number of text messages sent in a month is 2071.2, with a 95% confidence interval between 167.8 and 177.4 text messages.

Answer 2

• Between 503400 and 532200 text messages

----------------------------

Determine the average number of text messages sent per student within the margin of error

Find lower bound:

• 172.6 - 4.8 = 167.8 text messages

Find upper bound:

• 172.6 + 4.8 = 177.4 text messages

Estimate the total number of text messages for all 3000 students

Lower bound:

• 167.8 text messages × 3000 students = 503400 text messages

Upper bound:

• 177.4 text messages × 3000 students = 532200 text messages

The estimated number of text messages sent in a month for all 3000 high-school students in the city is:

• Between 503400 and 532200 text messages