Between 1954 and 2003, 42 different swimmers have crossed Lake Ontario. Both men
ID: 3053263 • Letter: B
Question
Between 1954 and 2003, 42 different swimmers have crossed Lake Ontario. Both men and women have made the crossing. For the 22 women, x = 1272 and s = 261 minutes. For the 20 males, x = 1197 and s = 304 minutes. Boxplots of the two data sets showed symmetric distributions with very different spreads. Compute and interpret a 95% confidence interval for the difference in mean times between male and female swimmers.
(a) Should you use the pooled procedure or unpooled procedure? Why?
b) If you use the unpooled procedure what is the value of the degrees of freedom?
(c) Compute a 95% confidence interval for the difference in swim times between men and women. Regardless of your answer to (a), use the unpooled procedure and use women - men.
(d) Write a sentence interpreting your interval from part (a). Be specific about the meaning in context.
(e) Does this confidence interval suggest that the mean swim times for men and women differ? Why or why not?
Explanation / Answer
a) Here the two samples are independent and taken from two different populations hence variation/std. dev. is not same. Hence we use unpooled procedure.
b)
DF = 38
c)
d)
From the above confidence interval we can interpret that there is 95% probability that the difference in mean time to swim is between -102.8383 and 252.8383
e)
As 0 is included in the CI, we can conclude that there is no difference in the mean swim times for men and women.
x1(bar) 1272.00 x2(bar) 1197.00 s1 261.00 s2 304.00 n1 22 n2 20 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 3096.4091 (s22/n2) 4620.8000 SE 87.8476 DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } [ (s12 / n1)2 / (n1 - 1) ] 456559.488 [ (s22 / n2)2 / (n2 - 1) ] 1123778.56 (s12/n1 + s22/n2)2 59555316.15 DF = 38Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.