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a)
To explain necessity of the conditions.
a)
Answer to Problem 33E
When the
Explanation of Solution
Given:
When constructing a confidence interval for a population proportion, we check that the sample size is less than 10% of the population size.
The conditions of sample size are important because when the sample size <10% of the population size then the observations in the sample are closer to independent.
It is not possible to correctly calculate standard deviation of sampling distribution of the sample proportions if the observations are not independent.
b)
To explain what happen if population size will not less than 10%.
b)
Answer to Problem 33E
The confidence interval will be inaccurate.
Explanation of Solution
Given:
When constructing a confidence interval for a population proportion, we check that the sample size is less than 10% of the population size.
The conditions of sample size are important because when the sample size <10% of the population size then the observations in the sample are closer to independent.
It is not possible to correctly calculate standard deviation of sampling distribution of the sample proportions if the observations are not independent.
Therefore, if standard deviation is incorrect then the required confidence interval will be inaccurate and there will be less chances to get population parameter in the confidence interval.
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