Determining Sample Size. In Exercises 19-22, assume that...

Determining Sample Size. In Exercises $19-22,$ assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 7-2 on page 338 to find the indicated sample size. Statistics Student Incomes You want to estimate the standard deviation of the annual incomes of all current statistics students. Find the minimum sample size needed to be $95 \%$ confident that the sample standard deviation is within $20 \%$ of the population standard deviation. Are those incomes likely to satisfy the requirement of a normal distribution?

Determining Sample Size. In Exercises $19-22,$ assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 7-2 on page 338 to find the indicated sample size.
Statistics Student Incomes You want to estimate the standard deviation of the annual incomes of all current statistics students. Find the minimum sample size needed to be $95 \%$ confident that the sample standard deviation is within $20 \%$ of the population standard deviation. Are those incomes likely to satisfy the requirement of a normal distribution?

Key Concepts

Simple Random Sampling

Simple random sampling is a method in which every member of a population has an equal chance of being selected. It is used to minimize bias, ensuring that the sample accurately represents the population, which is crucial for valid statistical inference.

Normal Distribution

The normal distribution is a continuous probability distribution that is symmetric about its mean, featuring the characteristic bell-shaped curve. Many statistical methods assume normality because of its well-known properties, which aid in deriving inference, especially for techniques involving variance estimation.

Confidence Interval for Variance/Standard Deviation

A confidence interval for a population’s variance or standard deviation provides a range that is likely to contain the true value of the parameter. When the data are normally distributed, the chi-square distribution is used to construct these intervals, allowing researchers to determine how much uncertainty is present in the estimated variability.

Sample Size Determination

Sample size determination is the process of calculating the minimum number of observations needed to achieve a desired level of precision in the estimation of a parameter. For estimating variance or standard deviation, the goal is often to ensure that the sample estimate falls within a specified percentage of the population value with a given level of confidence.

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