Question

2. In a random sample of 87 college students, the average number of GroupMe messages handled in
one day is 49. The 95% confidence interval for the mean number of messages handled by students
daily is given as 47 to 51.
a. What is the population standard deviation of the sample?
b. If the number of samples were doubled, by what factor would the confidence interval change
(keeping the same confidence level?)

Answer 1

We have that the population standard deviation and  confidence interval is mathematically given as

SD=1

W = 2.8284

Standard deviation and the new width

a) Generally, normal distribution 95% of the values lies within 2 standard deviations from the mean.

Therefore, we have here:

2*2SD = 51 - 47

2*2SD

SD=1

Hence, the standard deviation is

SD=1

b)

Where,the margin of error is inversely proportional to the square root of sample size.

1 / sqrt{2}

Hence, the new width is

1 / sqrt{2}$1 \ sqrt{2}$

W = 2.8284

For more information on Width visit

https://brainly.com/question/2096451