Question

Describe the relationship between the width of a confidence interval and the size of the sample. Also describe the relationship between the width of the confidence interval and the degree of confidence. If a study yields an unsatisfactorily large confidence interval, what should be done? What prevents a researcher from continually increasing the sample size until a very small confidence interval is achieved?

Answer 1

The relationship between the width of a confidence interval and the sample size:

• As we increase the sample size, the width of the interval gradually decreases.
• Mathematically.

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The relationship between the width of the confidence interval and the degree of confidence:

• As the width of interval becomes larger, the degree of confdence also increases.
• Mathematically,

NOTE: Degree of confidence is the probability that the interval will capture the true parameter.

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If a study yields an unsatisfactorily large confidence interval,

• We should increase the sample size. that help in gaining more information so that confidence interval become smaller.
• We can decrease the level of significance which is the probability of rejection of hypothesis when it is true.

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The restrictions a researcher from continually increasing the sample size until a very small confidence interval is achieved are:

• Increasing the sample size increases the cost in collection, man power and at the same time increases the time taken.
• The resources from which the samples are being collected are one of the major restrictions.
• Increasing the sample size also leads to the chances of error that is a Type 2 error which is the probability of acceptance of hypothesis when it is actually false.

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