Question

18. A study examines the relationship between hours of sleep and the level of relaxation one feels in the afternoon in a SAMPLE of women. One group was allowed to sleep between 5 and 6 hours and the other group was allowed to sleep between 7 and 8 hours.

Here are the data for both groups:

            5-6 hours of sleep                                7-8 hours of sleep       

           4, 1, 5, 10, 5, 10                                    3, 2, 9, 15, 1, 12

Calculate the following by hand:

            Calculate the mean for the 5-6 hour group. Answer______________________

            Calculate the mean for the 7-8 hour group. Answer:_______________________

            Calculate the standard deviation for the 5-6 hour group. Answer: ____________

            Calculate the standard deviation for the 7-8 hour group. Answer:_____________

            What can you say about the differences/similarities in the descriptive statistics between the groups?

Answer 1

1) mean for 5-6 hour group

mean=xi/n

=30/6

mean=5.8333

var(x)={(4-5.833)^2+(1-5.833)^2+(5-5.8333)^2+(10-5.8333)^2+(5-5.8333)^2+(10-5.5833)^2}/5

var(x)=12.5666

standad deviation=sqrt(var(x))

standard deviation=sqrt(12.5666)

standard deviation=3.5449

2) mean for 7-8 hour group

mean=xi/n

=42/7

mean=6

var(x)=(3-7)^2+(2-7)^2+(9-7)^2+(15-7)^2+(1-7)^2+(12-7)^2

=34

standard deviation=sqrt(34)

standard deviation=5.83095