(12 points) Between 1954 and 2003, 42 different swimmers have crossed Lake Ontar
ID: 2907833 • Letter: #
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(12 points) Between 1954 and 2003, 42 different swimmers have crossed Lake Ontario. Both men and women have made the crossing. For the 22 women, x1 = 1271.6 and s1 = 261 minutes. For the 20 males, x2 = 1196.8 and s2 = 304.4 minutes. Assuming that these swimmers represent a random sample of all swimmers, test the null hypothesis that the times are faster for men than women. Use the un-pooled test.
(a) (1 point) Why is the un-pooled procedure more appropriate in this situation?
(b) (2 points) State your hypotheses in words and using proper mathematical symbols and notation.
(c) (4 points) Compute your test statistic and state the degrees of freedom. Round your test statistic to two decimal places.
(d) (3 points) Find the p-value and give a p-value range. (e) (2 points) State your conclusion in context using ? = 0.05.
(12 points) Between 1954 and 2003, 42 different swimmers have crossed Lake Ontario. Both men and women have made the crossing. For the 22 women, 127 1.6 and 81-261 minutes. For the 20 males, 22-1196.8 and s2 304.4 minutes. Assuming that these swimmers represent a radom sample of all swimmers, test the null hypothesis that the times are faster for men than women. Use the un-pooled test. (a) (1 point) Why is the un-pooled procedure more appropriate in this situation? (b) (2 points) State your hypotheses in words and using proper mathematical symbols and notation. (c) (4 points) Compute your test statistic and state the degrees of freedom. Round your test statistic to two decimal places. (d) (3 points) Find the p-value and give a p-value range (e) (2 points) State your conclusion in context using a 0.05Explanation / Answer
a)
the population variances are very different (that is sigma1^2is not equal to sigma2^2), then we used the unpooled t-test
b)
H0 : mu2 = mu1
Ha : mu2 < mu1
c)
t = (x2 -x1)/sqrt(s2^2/n2 + s1^2/n1)
= (1196.8 - 1271.6)/sqrt(304.4^2/20 + 261^2/22)
= -0.85
df = 20 - 1 = 19
d)
p value = .2029
There is not sufficient evidence to support the claim that the times are faster for men than women.
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