1) A statistics professor at a large university had an assignment where his students would sample from the population of all the students at the college living on campus....

Question

1) A statistics professor at a large university had an assignment where his students would sample from the population of all the students at the college living on campus. Each of his 400 students used a computer program to select a random sample of students living on campus, and the search also returned the number of credits the selected students were taking. Each student then took their sample of credits and used Stat key to make 90% confidence interval estimates for the population mean number of credits being taken by students living on campus. Of the 400 statistics students who did this, how many of the intervals would be roughly the number we would expect to “work”, or, the number we would expect to actually contain the population mean value? (select your answer but show the little/quick work to support it!) 

a)270

b) 335

c) 360

d) 395

Answer 1

Answer: We would expect approximately 360 intervals to capture the population mean.

Explanation: There are two main steps to solving a problem like this

1. Convert the % confidence into a decimal by taking: % confidence/100
2. Multiply your confidence (as a decimal from Step #1) times the sample size (number of intervals)

Therefore, for this specific problem, the work would look like:

1.90%/100 = 0.90

2.(0.90) x (400) = 360

As a result, we would expect 360 of the sampling intervals to capture the true population mean.