Sample Statistic

Definition

A sample statistic is a numerical value calculated from a sample of data that is used to estimate or describe a characteristic of the larger population. It serves as a representation of the population parameter and is crucial in statistical inference and decision-making.

5 Must Know Facts For Your Next Test

1. Sample statistics are used to make inferences about population parameters, such as the population mean or proportion.
2. The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as the sample size increases.
3. The finite population correction factor adjusts the standard error of a sample statistic when the sample size is a significant proportion of the total population size.
4. The null hypothesis in a hypothesis test is a statement about the value of a population parameter, and the sample statistic is used to evaluate the plausibility of the null hypothesis.
5. The alternative hypothesis in a hypothesis test is the statement that the population parameter is different from the value specified in the null hypothesis, and the sample statistic is used to determine if there is sufficient evidence to reject the null hypothesis.

Review Questions

• Explain how the Central Limit Theorem relates to the use of sample statistics in making inferences about population parameters.
  • The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution. This allows us to use sample statistics, such as the sample mean, to make inferences about the population mean, as the sample statistic will be approximately normally distributed and can be used to construct confidence intervals and perform hypothesis tests about the population parameter.
• Describe the role of the finite population correction factor in the use of sample statistics when the sample size is a significant proportion of the total population size.
  • When the sample size is a significant proportion of the total population size, the finite population correction factor should be applied to the standard error of the sample statistic. This factor adjusts the standard error to account for the fact that the sample is being drawn from a finite population, rather than an infinite population. The finite population correction factor reduces the standard error of the sample statistic, leading to more precise inferences about the population parameter.
• Analyze how sample statistics are used to formulate and evaluate null and alternative hypotheses in hypothesis testing.
  • In hypothesis testing, the null hypothesis is a statement about the value of a population parameter, such as the population mean or proportion. The sample statistic is used to evaluate the plausibility of the null hypothesis. If the sample statistic is significantly different from the value specified in the null hypothesis, there is evidence to reject the null hypothesis in favor of the alternative hypothesis, which states that the population parameter is different from the value in the null hypothesis. The sample statistic is the key piece of information used to determine whether the null hypothesis should be rejected or not, and thus plays a crucial role in the hypothesis testing process.

Related terms

Population Parameter: A numerical value that describes a characteristic of the entire population, such as the population mean or population proportion.

Sampling Distribution: The distribution of all possible values of a sample statistic that could be obtained from the population.

Standard Error: The standard deviation of the sampling distribution of a sample statistic, which measures the variability of the sample statistic around the population parameter.