The height is measured for U.S. adult males and U.S. adult females. The sample o
ID: 3150406 • Letter: T
Question
The height is measured for U.S. adult males and U.S. adult females. The sample of 15 males had an average height of 68 inches and the sample of 25 females had an average height of 61.8 inches. Assume the population standard deviation is 2.5 inches for male and 2.1 inches for female. (Please Show Work)
We believe that the males are taller than females on average. Test the claim at the 0.01 level of significance. Use males as "Population 1" and females as "Population 2."
(a) What type of test is this?
fluffy-tailed left-tailed two-tailed right-tailed
(b) What is the test statistic?
(round your answer to two decimal places)
It is recommended that you submit your answers for parts a and b before submitting your answers for parts c and d below.
(c) What is the statistical decision?
Reject H0? Fail to reject H0? Reject Ha? Fail to reject Ha?
Again, you may want to submit your answer for part c before submitting your answer for part d.
(d) This means we ....can? cannot? might? always? never? ....conclude that the population mean height of males is higher than the population mean height of females.
(e) Now create a 99% confidence interval for the difference between population mean height of males and females.
99% CI = ? to ?
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 <= 0
Ha: u1 - u2 > 0
At level of significance = 0.01
As we can see, Ha used > (as males are believed to be taller) this is a right tailed test.
[ANSWER: RIGHT TAILED]
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b)
Calculating the means of each group,
X1 = 68
X2 = 61.8
Calculating the standard deviations of each group,
s1 = 2.5
s2 = 2.1
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 15
n2 = sample size of group 2 = 25
Thus, df = n1 + n2 - 2 = 38
Also, sD = 0.770108218
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 8.050816572 [ANSWER]
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c)
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = 2.428567631
Also, using p values,
p = 4.88602E-10
As t > 2.429, and P < 0.01, WE REJECT THE NULL HYPOTHESIS.
ANSWER: REJECT HO [ANSWER]
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D)
(d) This means we CAN conclude that the population mean height of males is higher than the population mean height of females. [answer]
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e)
For the 0.99 confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.005
t(alpha/2) = 2.711557602
lower bound = [X1 - X2] - t(alpha/2) * sD = 4.111807209
upper bound = [X1 - X2] + t(alpha/2) * sD = 8.288192791
Thus, the confidence interval is
( 4.111807209 , 8.288192791 ) [ANSWER]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!
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