iven in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 0.01 significance level for both parts. Male BMI Female BMI mu μ mu 1 μ1 mu 2 μ2 n 43 43 43 43 x overbar x 27.4044 27.4044 24.7189 24.7189 s 7.233502 7.233502 4.426471 4.426471 a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? A. Upper H 0 H0: mu 1
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Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from 0.01 0.01 significance level for both parts. |
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|
Male BMI |
Female BMI |
|
|
|
|
mu μ |
mu 1 μ1 |
mu 2 μ2 |
|
|
|
|
n |
43 43 |
43 43 |
|
|
|
|
x overbar x |
27.4044 27.4044 |
24.7189 24.7189 |
|
|
|
|
s |
7.233502 7.233502 |
4.426471 4.426471 |
|
a. Test the claim that males and females have the same
What are the null and alternative hypotheses?
A.
Upper H 0
H0:
mu 1
μ1
equals
=
mu 2
μ2
Upper H 1
H1:
mu 1
μ1
not equals
≠
mu 2
μ2
B.
Upper H 0
H0:
mu 1
μ1
not equals
≠
mu 2
μ2
Upper H 1
H1:
mu 1
μ1
less than
<
mu 2
μ2
C.
Upper H 0
H0:
mu 1
μ1
equals
=
mu 2
μ2
Upper H 1
H1:
mu 1
μ1
greater than
>
mu 2
μ2
D.
Upper H 0
H0:
mu 1
μ1
greater than or equals
≥
mu 2
μ2
Upper H 1
H1:
mu 1
μ1
less than
<
mu 2
The test statistic, t, is ___
The P-value is ____
State the conclusion for the test.
A. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
B.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
C.
Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
D.Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.
b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.
___< μ1 - μ2<___
(Round to three decimal places as needed.)
Does the confidence interval support the conclusion of the test?
_____ because the confidence interval contains____
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