In: Statistics and Probability
Respondents in the 2017 General Social Survey (GSS) were asked “on an average work day, about how many hours do you have to relax or pursue the activities that you enjoy?”. 244 males responded to the question and 262 females responded. Men reported an average of 3.28 hours per day (with a standard deviation of 2.12 hours) and women reported an average of 2.99 hours per day (sd=2.05).
A. Calculate and interpret the 95% confidence interval for relaxation hours for men.
B. Calculate and interpret the 95% confidence interval for relaxation hours for women.
C. Using the data from Parts A and B, how do men and women in the population compare in terms of time spent relaxing?
A) Mean ()
= 3.28
Sample size (n) = 244
Standard deviation (s) = 2.12
Confidence interval(in %) = 95
z @ 95.0% = 1.96
Since we know that
Required confidence interval = (3.28-0.266, 3.28+0.266)
Required confidence interval = (3.014, 3.546)
We are 95% confident that the true mean of number of hours men
spend relax or pursue the activities that they enjoy everyday in
the calculated interval.12.
B) Mean ()
= 2.99
Sample size (n) = 262
Standard deviation (s) = 2.05
Confidence interval(in %) = 95
z @ 95.0% = 1.96
Since we know that
Required confidence interval = (2.99-0.2482, 2.99+0.2482)
Required confidence interval = (2.7418, 3.2382)
We are 95% confident that the true mean of number of hours women
spend relax or pursue the activities that they enjoy everyday in
the calculated interval.
C Fom the 2 confidence interval we can say that the confidence
interval for men is bigger, also it seems like men tends to
relax/pursue the activities they enjoy for more time.
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