CONFIDENCE INTERVAL

CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN TWO POPULATION MEANS

 

EXERCISES

 

For each of the following exercises construct 90,95, and 99 percent confidence intervals for the difference between population means. Where appropriate, state the assumptions that  make your method valid. State the practical and probabilistic interpretations of each interval that you construct. Consider the variables under consideration in each exercise, and state what use you think researchers might make of your results.

 

6.4.1: The objective of an experiment was to study effect of pancuronium-induced  muscle relaxation on circulating plasma volume. Subjects were newborn infants weighing more than 1700 grams who required respiratory assistance within 24 hours of birth and met other clinical criteria. Five infants paralyzed with pancuronium and seven nonparalyzed infants yielded the following statistics on the second of three measurements of plasma volume (ml) made during mechanical ventilation:

 

Subject group                     Sample mean                       Sample standard deviation

 

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Paralyzed                                    48.0                                            8.1

 

Nonparalyzed                             56.7                                             8.1

 

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The second measurement for the paralyzed group occurred 12 to 24 hours after the first dose of pancuronium. For the nonparaslyzed group. Measurements were made 12 to 24 hours after commencing mechanical ventilation.

 

ANSWER

 

(a)    0.1035 , 17.2964

 

(b)   8.1324, 29.2676

 

(c)    -6.3316, 23.7316

 

 

CONFIDENCE INTERVAL FOR A POPULATION PROPORTION

 

EXERCISES

 

For each of the following exercises state the practical and probabilistic interpretation of the interval that you construct. Identify each component of the interval: point estimate, reliability coefficient, and standard error. Explain why the reliability coefficients are not the same for all exercises.

 

6.5.1: In a study of childhood abuse in psychiatric patients, note that 166 in a sample of 947 patients reported histories physical and/or sexual abuse. Construct a 90 percent confidence interval for the population proportion.

 

ANSWER

 

0.1511, 0.1995

 

6.5.3: In a study of the effect on birth weight  of maternal stress during pregnancy. Subjects were 86 white mothers with a history of stress who had no known medical or obstetric risk factors for reduced birth weight. The investigators found that 12.8 percent of the mothers in the study gave birth to babies satisfying the criterion for low birth weight. Construct 99 percent confidence interval for the population proportion.

 

ANSWER

 

0.035, 0.221

 

CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN TWO POPULATION PROPORTION

 

EXERCISES

 

6.6.3: A sample of 67 physicians and 133 nurses with chemical dependent significant others. The purpose of the study was to evaluate the effect on physicians and nurses of being closely involved with one or more chemical-dependent persons. Fifty two of the physicians and 89 of the nurses said that living with a chemical – dependent person adversely affected their work. State all assumptions that you think are necessary and construct a 95 percent confidence interval for the difference between the proportions in the two populations whose work we would expect to be adversely affected by living with chemical dependent person.

 

ANSWER

 

-0.0210, 0.2348