Question

A survey is done to check how much time students actually spend working on the course outside the class. 29 randomly selected students are asked: "How many hours of schoolwork do you do outside of class for each hour in class?" The sample mean of the 29 respondents is 1.2 hours with a standard deviation of 0.24 hours.

1. What is the standard error of the sample mean x¯x¯? [answer to 3 decimal places]

2. Suppose μμ denotes the population mean hours students spend outside class. Which of the following options gives the formula for 99% confidence interval for μμ?
a. x¯∓1.7×s.e.(x¯)x¯∓1.7×s.e.(x¯)
b. x¯∓2.76×s.e.(x¯)x¯∓2.76×s.e.(x¯)
c. x¯∓2.47×s.e.(x¯)x¯∓2.47×s.e.(x¯)
d. x¯∓2.05×s.e.(x¯)x¯∓2.05×s.e.(x¯)
e. x¯∓1.31×s.e.(x¯)x¯∓1.31×s.e.(x¯)

3. What is the margin of error of the 99% confidence interval of μμ? [answer to 3 decimal places]

4. The students are advised at the start of the semester that they are supposed to spend 2 hours working outside of class for each hour in class. Based on the above 99% confidence interval for μμ are the students working less than the suggested hours?
a. no, because the 99% confidence interval for μμ is not entirely below 2
b. yes, because the entire 99% confidence interval for μμ is below 2
c. yes, because μ<2μ<2
d. yes, because x¯<2x¯<2

Answer 1

1)

standard errror of mean =

sx=s/√n=

0.045

2)

b. x¯∓2.76×s.e

3)

margin of error of the 99% confidence interval of μ =2.76*0.045 =0.124 ( please try 0.123 if this comes wrong due to rounding error)

4)

b. yes, because the entire 99% confidence interval for μμ is below 2