Essential Statistics
Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Chapter 9, Problem 5CS
To determine

Check whether the results obtained in Exercise-2 are same with the results obtained in Exercise-4.

Expert Solution & Answer
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Answer to Problem 5CS

Yes, the results obtained in Exercise-2 are same with the results obtained in Exercise-4.

Explanation of Solution

Calculation:

The data represents the means and standard deviations corresponding to three characteristics of standard treatment and new treatment.

Furthermore, the data corresponding to the percentage with the characteristics for the 5 characteristics for standard treatment and new treatment is given.

Here, it is given that the sample size of standard treatment is n1=731 and the sample size of new treatment is n2=1,089.

x¯i's are the sample means of each characteristics and si's are the sample standard deviations of each characteristics. μi's be the population means of each characteristics.

Hypothesis test for the variable “Age”:

The hypotheses are given below:

Null hypothesis:

H0:μ1=μ2

That is, there is no significant difference between the mean age of new treatment and standard treatment.

Alternate hypothesis:

H1:μ1μ2

That is, there is a significant difference between the mean age of new treatment and standard treatment.

Hypothesis test for the variable “Systolic blood pressure”:

The hypotheses are given below:

Null hypothesis:

H0:μ1=μ2

That is, there is no significant difference between the mean systolic blood pressure of new treatment and standard treatment.

Alternate hypothesis:

H1:μ1μ2

That is, there is a significant difference between the mean systolic blood pressure of new treatment and standard treatment.

Hypothesis test for the variable “Diastolic blood pressure”:

The hypotheses are given below:

Null hypothesis:

H0:μ1=μ2

That is, there is no significant difference between the meandiastolic blood pressure of new treatment and standard treatment.

Alternate hypothesis:

H1:μ1μ2

That is, there is a significant difference between the meandiastolic blood pressure of new treatment and standard treatment.

Hypothesis test for the variable “Treatment for hypertension”:

The hypotheses are given below:

Null hypothesis:

H0:p1=p2

That is, there is no significant difference between the proportion of treatment for hypertension under new treatment and standard treatment.

Alternate hypothesis:

H1:p1p2

That is, there is a significant difference between the proportion of treatment for hypertension under new treatment and standard treatment.

Hypothesis test for the variable “Atrial fibrillation”:

The hypotheses are given below:

Null hypothesis:

H0:p1=p2

That is, there is no significant difference between the proportion of Atrial fibrillation under new treatment and standard treatment.

Alternate hypothesis:

H1:p1p2

That is, there is a significant difference between the proportion of Atrial fibrillation under new treatment and standard treatment.

Hypothesis test for the variable “Diabetes”:

The hypotheses are given below:

Null hypothesis:

H0:p1=p2

That is, there is no significant difference between the proportion of Diabetes under new treatment and standard treatment.

Alternate hypothesis:

H1:p1p2

That is, there is a significant difference between the proportion of Diabetes under new treatment and standard treatment.

Hypothesis test for the variable “Cigarette smoking”:

The hypotheses are given below:

Null hypothesis:

H0:p1=p2

That is, there is no significant difference between the proportion of Cigarette smoking under new treatment and standard treatment.

Alternate hypothesis:

H1:p1p2

That is, there is a significant difference between the proportion of Cigarette smoking under new treatment and standard treatment.

Hypothesis test for the variable “Coronary bypass surgery”:

The hypotheses are given below:

Null hypothesis:

H0:p1=p2

That is, there is no significant difference between the proportion of Coronary bypass surgery under new treatment and standard treatment.

Alternate hypothesis:

H1:p1p2

That is, there is a significant difference between the proportion of Coronary bypass surgery under new treatment and standard treatment.

The results obtained in Exercise-2 are as follows:

Decision rule based on P-value:

If Pvalueα, then reject the null hypothesis H0.

If Pvalue>α, then fail to reject the null hypothesis H0.

CharacteristicP–value

Relation with

P–value and α

Acceptance of rejection

of null hypothesis

Age0.0570.057(=P)>0.05(=α)Fail to reject the null hypothesis
Systolic blood pressure0.0000.000(=P)<0.05(=α)

Reject the null

hypothesis

Diastolic blood pressure0.0370.037(=P)<0.05(=α)

Reject the null

hypothesis

Treatment for hypertension0.8190.819(=P)>0.05(=α)Fail to reject the null hypothesis
Atrial fibrillation0.3370.337(=P)>0.05(=α)Fail to reject the null hypothesis
Diabetes0.8750.875(=P)>0.05(=α)Fail to reject the null hypothesis
Cigarette smoking0.3430.343(=P)>0.05(=α)Fail to reject the null hypothesis
Coronary bypass surgery0.7620.762(=P)>0.05(=α)Fail to reject the null hypothesis

Conclusions:

There is no significant difference between the mean age of new treatment and standard treatment.

There is a significant difference between the mean systolic blood pressure of new treatment and standard treatment.

There is a significant difference between the mean diastolic blood pressure of new treatment and standard treatment.

There is no significant difference between the proportion of treatment for hypertension under new treatment and standard treatment.

There is no significant difference between the proportion of Atrial fibrillation under new treatment and standard treatment.

There is no significant difference between the proportion of cigarette smoking under new treatment and standard treatment.

There is no significant difference between the proportion of coronary bypass surgery under new treatment and standard treatment.

From this it is known that, the assignments to the groups are not balanced for the health characteristics “Systolic blood pressure” and “Diastolic blood pressure”.

Thus, the assignments to the groups are not balanced for the health characteristics “Systolic blood pressure” and “Diastolic blood pressure”.

The results obtained in Exercise-4 are as follows:

Decision in the given scenario:

If “0” lies between the confidence interval, then fail to reject the null hypothesis H0.

If “0” does not lie between the confidence interval, then reject the null hypothesis H0.

Conclusion based on confidence intervals:

CharacteristicP–valueWhether or not “0” lies in the confidence interval

Acceptance of rejection

of null hypothesis

Age(2.032,0.032)_

“0” lies in the

confidence interval

Fail to reject the null hypothesis
Systolic blood pressure(4.651,1.349)_

“0” does not lie in the

confidence interval

Reject the null

hypothesis

Diastolic blood pressure(1.938,0.062)_

“0” does not lie in the

confidence interval

Reject the null

hypothesis

Treatment for hypertension(0.0504,0.0399)_

“0” lies in the

confidence interval

Fail to reject the null hypothesis
Atrial fibrillation(0.0157,0.0452)_

“0” lies in the

confidence interval

Fail to reject the null hypothesis
Diabetes(0.0467,0.0396)_

“0” lies in the

confidence interval

Fail to reject the null hypothesis
Cigarette smoking(0.016,0.0455)_

“0” lies in the

confidence interval

Fail to reject the null hypothesis
Coronary bypass surgery(0.04895,0.03585)_

“0” lies in the

confidence interval

Fail to reject the null hypothesis

Conclusions:

There is no significant difference between the mean age of new treatment and standard treatment.

There is a significant difference between the mean systolic blood pressure of new treatment and standard treatment.

There is a significant difference between the mean diastolic blood pressure of new treatment and standard treatment.

There is no significant difference between the proportion of treatment for hypertension under new treatment and standard treatment.

There is no significant difference between the proportion of Atrial fibrillation under new treatment and standard treatment.

There is no significant difference between the proportion of cigarette smoking under new treatment and standard treatment.

There is no significant difference between the proportion of coronary bypass surgery under new treatment and standard treatment.

From this it is known that, the assignments to the groups are not balanced for the health characteristics “Systolic blood pressure” and “Diastolic blood pressure”.

Thus, the assignments to the groups are not balanced for the health characteristics “Systolic blood pressure” and “Diastolic blood pressure”.

From the above conclusions, it is clear that that the results obtained in Exercise-2 are same with the results obtained in Exercise-4.

The close relationship between confidence interval and testing of hypothesis sates that, if the value of the population parameter mentioned in the null hypothesis is contained in the 95% interval then the null hypothesis cannot be rejected at 5% level. If the value specified by the null hypothesis is not in the interval then the null hypothesis can be rejected at 5% level.

Thus, the results obtained in Exercise-2 are same with the results obtained in Exercise-4.

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Chapter 9 Solutions

Essential Statistics

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