Question

In a study to explore the possibility of hormonal alteration in asthma, data were collected on 22

postmenopausal women with asthma and 22 postmenopausal women without asthma.

Dehydroepiandrosterone sulfate (DHEAS) values were collected by the investigators.Use hypothesis

testing to determine if the mean DHEAS for postmenopausal women with asthma is larger than the mean

DHEAS for postmenopausal women without asthma.Assume that DHEAS is normally distributed and

that the population variances are equal.

Group	Method	N	Mean	Std Dev		Std Err	Minimum		Maximum
Asthma		22	108.0	60.0064	12.7934			25.1600	241.9
No_Asth		22	56.0877	42.9782	9.1630			6.6400	166.0
Diff (1-2)	Pooled		51.8977	52.1915	15.7363
Diff (1-2)	Satterthwaite		51.8977		15.7363

Method	Variances	DF	t Value	Pr > t
Pooled	Equal	42	3.30	0.0010
Satterthwaite	Unequal	38.057	3.30	0.0011

a. What are the null and alternative hypotheses? Be sure to define any symbols that you use.

b.underline the following for testing that the mean DHEAS is greater for those with asthma than those without asthma and fill in the blanks.

test statistic _______________          degrees of freedom _______________          p-value ________________

1.   Based on your answer in part b, what is the result of the test? Circle or underline your answer.

                                    Reject H₀                                Fail to Reject H₀

2. State your conclusion from the hypothesis test in the context of the applied problem.

c. underline the following and fill in the blanks.

Point estimate of difference between population means ______________

Pooled standard deviation ______________

Answer 1

NULL HYPOTHESIS H0: the mean DHEAS for postmenopausal women with asthma is larger than the mean DHEAS for postmenopausal women without asthma

ALTERNATIVE HYPOTHESIS Ha:the mean DHEAS for postmenopausal women with asthma is larger than the mean DHEAS for postmenopausal women without asthma . $\mu (a)>\mu(w.a)$

b) Test statistic= 3.30

degrees of freedom= 42

Pvalue= 0.0010

REJECT H0

CONCLUSION. WE REJECT NULL HYPOTHESIS. WE HAVE SUFFICIENT EVIDENCE TO SHOW THAT the mean DHEAS for postmenopausal women with asthma is larger than the mean DHEAS for postmenopausal women without asthma.

POINT ESTIMATE OF DIFERENCE= 51.9123

POOLED STANDARD DEVIATION= 52.1915