Question 1198771: A random sample of 150 college students regarding their work schedules produce a
mean of 25.4 hours worked per week with a standard deviation of 12 hours.
a) What is the point estimate of mean time worked per week? Calculate margin of
error when α = 0.01.
b) Construct a 95% confidence interval for the mean number of hours worked per week
by college students
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a) What is the point estimate of mean time worked per week? Calculate margin of
error when α = 0.01.
the point estimate of the mean time worked per week is the mean of the sample which is equal to 25.4 hours worked per week.
the margin of error when alpha = .01 is found by using the t-score as follows:
note that you are using the t-score rather than the z-score because the standard deviation is taken from the sample rather than from the population.
t-score formula is:
t = (x-m)/s
t is the t-score
x is the sample mean
m is the population mean
s is the standard error
standard error = standard deviation / square root of sample size = 12/sqrt(150) = .9797958971.
at two sided alpha of .01, the alpha on each side will be .01/2 = .005
at 149 degrees of freedom, the critical t-score will be plus or minus plus or minus 2.609227895.
use the plus value in the t-score formula to find the margin of error.
you will get:
2.609227895 = (x - 25.4) / .9797958971.
solve for x to get:
x = 2.609227895 * .9797958971 + 25.4 = 27.95651079.
subtract 25.4 from that to get margin of error = 2.556510786.
that's your margin of error.
b) Construct a 95% confidence interval for the mean number of hours worked per week by college students.
95% confidence interval will have an alpha tail on each end equal to .05/2 = .025.
the critical t-score with 149 degrees of freedom will be plus or minus plus or minus 1.976013145.
when t = 1.976013145, t-score formula becomes 1.976013145 = (x - 25.4) / .9797958971.
solve for x to get:
x = 1.976013145 * 1.976013145 + 25.4 = 27.33608957.
when t = -1.976013145, t-score formula becomes -1.976013145 = (x - 25.4) / .9797958971.
solve for x to get:
x = -1.976013145 * 1.976013145 + 25.4 = 23.46391043.
your 95% confidence interval is from 23.46391043 to 27.33608957.
i've checked this a few times and i'm pretty sure this is correct.
let me know if you have any questions.
theo
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