Essential Statistics
Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Chapter 9, Problem 3CS
To determine

Find the 95% confidence interval for the group means or group proportions for the health characteristics.

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Answer to Problem 3CS

The 95% confidence intervals for the each of the characteristics are as follows:

Characteristic95% confidence interval
Age(2.032,0.032)_
Systolic blood pressure(4.651,1.349)_
Diastolic blood pressure(1.938,0.062)_
Treatment for hypertension(0.0504,0.0399)_
Atrial fibrillation(0.0157,0.0452)_
Diabetes(0.0467,0.0396)_
Cigarette smoking(0.016,0.0455)_
Coronary bypass surgery(0.04895,0.03585)_

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.

95% confidence interval for the variable “Age”:

Software Procedure:

Step by step procedure to find 95% confidence interval forthe difference between the two population means using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Sample t.
  • Choose Summarized data.
  • In first sample, enter the sample size as 731, sample mean as 64 and sample standard deviation as 11.
  • In second sample, enter the sample size as 1,089, sample mean as 65 and sample standard deviation as 11.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  1

From, the MINITAB output the 95% confidence interval for the difference between the mean age of new treatment and standard treatment is (2.032,0.032)_.

95% confidence interval for the variable “Systolic blood pressure”:

Software Procedure:

Step by step procedure to find 95% confidence interval forthe difference between the two population means using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Sample t.
  • Choose Summarized data.
  • In first sample, enter the sample size as 731, sample mean as 121 and sample standard deviation as 18.
  • In second sample, enter the sample size as 1,089, sample mean as 124 and sample standard deviation as 17.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  2

From, the MINITAB output the 95% confidence interval for the difference between the mean systolic blood pressure of new treatment and standard treatmentis (4.651,1.349)_.

95% confidence interval for the variable “Diastolic blood pressure”:

Software Procedure:

Step by step procedure to find 95% confidence interval for the difference between the two population means using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Sample t.
  • Choose Summarized data.
  • In first sample, enter the sample size as 731, sample mean as 71 and sample standard deviation as 10.
  • In second sample, enter the sample size as 1,089, sample mean as 72 and sample standard deviation as 10.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  3

From, the MINITAB output the 95% confidence interval for the difference between the mean diastolic blood pressure of new treatment and standard treatmentis (1.938,0.062)_.

95% confidence interval for the variable “Treatment for hypertension”:

The sample size of standard treatment is n1=731. The percentage with the characteristics “Treatment for hypertension under standard treatment” is p1=0.632.

Hence, the specified characteristics of treatment for hypertension under new treatment is x1=n1×p1=461.992.

The sample size of new treatment is n2=1,089. The percentage with the characteristics “Treatment for hypertension under new treatment” is p2=0.637.

Hence, the specified characteristics of treatment for hypertension under new treatment is x2=n2×p2=693.693.

Software Procedure:

Step by step procedure to find 95% confidence interval for the difference between the two population proportions using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Proportions.
  • Choose Summarized data.
  • In first sample, enter the number of trials as 731 and number of events as 462.
  • In second sample, enter the number of trials as 1,089 and number of events as 694.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  4

From, the MINITAB output the 95% confidence interval for the difference between the proportion of treatment for hypertension under new treatment and standard treatmentis (0.0504,0.0399)_.

95% confidence interval for the variable “Atrial fibrillation”:

The sample size of standard treatment is n1=731. The percentage with the characteristics “Atrial fibrillation under standard treatment” is p1=0.126.

Hence, the specified characteristics of treatment for Atrial fibrillation under standard treatment is x1=n1×p1=92.106.

The sample size of new treatment is n2=1,089. The percentage with the characteristics “Atrial fibrillation under new treatment” is p2=0.111.

Hence, the specified characteristics of Atrial fibrillation under new treatment is x2=n2×p2=120.879.

Software Procedure:

Step by step procedure to find 95% confidence interval for the difference between the two populationproportions using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Proportions.
  • Choose Summarized data.
  • In first sample, enter the number of trials as 731 and number of events as 92.
  • In second sample, enter the number of trials as 1,089 and number of events as 121.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  5

From, the MINITAB output the 95% confidence interval for the difference between the proportion of Atrial fibrillation under new treatment and standard treatment is (0.0157,0.0452)_.

95% confidence interval for the variable “Diabetes”:

The sample size of standard treatment is n1=731. The percentage with the characteristics “Diabetes under standard treatment” is p1=0.302.

Hence, the specified characteristics of diabetes under standard treatment is x1=n1×p1=220.762.

The sample size of new treatment is n2=1,089. The percentage with the characteristics “Diabetes under new treatment” is p2=0.306.

Hence, the specified characteristics of diabetes under new treatment is x2=n2×p2=333.234.

Software Procedure:

Step by step procedure to find 95% confidence interval for the difference between the two population proportions using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Proportions.
  • Choose Summarized data.
  • In first sample, enter the number of trials as 731 and number of events as 221.
  • In second sample, enter the number of trials as 1,089 and number of events as 333.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  6

From, the MINITAB output the95% confidence interval for the difference between the proportion of Diabetes under new treatment and standard treatment is (0.0467,0.0396)_.

95% confidence interval for the variable “Cigarette smoking”:

The sample size of standard treatment is n1=731. The percentage with the characteristics “Cigarette smoking under standard treatment” is p1=0.128.

Hence, the specified characteristics of cigarette smoking under standard treatment is x1=n1×p1=93.568.

The sample size of new treatment is n2=1,089. The percentage with the characteristics “Cigarette smoking under new treatment” is p2=0.114.

Hence, the specified characteristics of cigarette smoking under new treatment is x2=n2×p2=124.146.

Software Procedure:

Step by step procedure to find 95% confidence interval for the difference between the two population proportions using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Proportions.
  • Choose Summarized data.
  • In first sample, enter the number of trials as 731 and number of events as 94.
  • In second sample, enter the number of trials as 1,089 and number of events as 124.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  7

From, the MINITAB output the 95% confidence interval for the difference between the proportion of Cigarette smoking under new treatment and standard treatment is (0.016,0.0455)_.

95% confidence interval for the variable “Coronary bypass surgery”:

The sample size of standard treatment is n1=731. The percentage with the characteristics “Coronary bypass surgery under standard treatment” is p1=0.285.

Hence, the specified characteristics of Coronary bypass surgery under standard treatment is x1=n1×p1=208.335.

The sample size of new treatment is n2=1,089. The percentage with the characteristics “Coronary bypass surgery under new treatment” is p2=0.291.

Hence, the specified characteristics of coronary bypass surgery under new treatment is x2=n2×p2=316.899.

Software Procedure:

Step by step procedure to find 95% confidence interval for the difference between the two population proportions using the MINITAB software:

  • Choose Stat > Basic Statistics > 2-Proportions.
  • Choose Summarized data.
  • In first sample, enter the number of trials as 1,089 and number of events as 317.
  • In second sample, enter the number of trials as 731 and number of events as 208.
  • Choose Options.
  • In Confidence level, enter 95.
  • Enter 0 in Hypothesized value.
  • In Alternative, select not equal to
  • Click OK in all the dialogue boxes.

Output using the MINITAB software is given below:

Essential Statistics, Chapter 9, Problem 3CS , additional homework tip  8

From, the MINITAB output the 95% confidence interval for the difference between the proportion of Coronary bypass surgery under new treatment and standard treatment is (0.04895,0.03585)_.

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Chapter 9 Solutions

Essential Statistics

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