T-test

Definition

The t-test is a statistical hypothesis test that is used to determine if the mean of a population is significantly different from a hypothesized value or if the means of two populations are significantly different from each other. It is commonly used in scenarios where the population standard deviation is unknown, and the sample size is small.

5 Must Know Facts For Your Next Test

1. The t-test is used when the population standard deviation is unknown, and the sample size is small (typically less than 30).
2. The t-test statistic follows a t-distribution, which is similar to the standard normal distribution but has heavier tails.
3. The t-test can be used to test hypotheses about a single population mean, the difference between two population means, or the relationship between variables.
4. The choice of a one-tailed or two-tailed t-test depends on the specific hypothesis being tested.
5. The t-test is a powerful tool for making inferences about population parameters when the underlying distribution is approximately normal.

Review Questions

• Explain how the t-test is used in the context of a confidence interval for home costs.
  • In the context of a confidence interval for home costs (topic 8.4), the t-test is used to construct a confidence interval for the mean home cost in a population when the population standard deviation is unknown. The t-test statistic is calculated using the sample mean, sample standard deviation, and sample size, and the resulting confidence interval provides a range of values that is likely to contain the true population mean home cost. This allows researchers or policymakers to make inferences about the typical home cost in a region or community, even when the exact population standard deviation is not known.
• Describe how the t-test is used to test null and alternative hypotheses (topic 9.1) about a population mean or proportion.
  • The t-test is a key tool in hypothesis testing (topic 9.1) when the population standard deviation is unknown. In this context, the t-test is used to determine whether the sample data provides sufficient evidence to reject a null hypothesis about a population mean or proportion in favor of an alternative hypothesis. The test statistic is calculated using the sample data and compared to a critical value from the t-distribution to decide whether to reject or fail to reject the null hypothesis. This allows researchers to make inferences about population parameters based on sample information, while accounting for the uncertainty introduced by small sample sizes.
• Analyze how the t-test is used in the hypothesis testing of a single mean or single proportion (topic 9.6).
  • In the hypothesis testing of a single mean or single proportion (topic 9.6), the t-test is used to determine whether the sample data provides sufficient evidence to conclude that the population mean or proportion is significantly different from a hypothesized value. The t-test statistic is calculated using the sample mean or proportion, the hypothesized value, and the standard error of the sample. This statistic is then compared to a critical value from the t-distribution to decide whether to reject or fail to reject the null hypothesis. The t-test allows researchers to make inferences about the population parameter while accounting for the uncertainty inherent in small samples, making it a crucial tool for drawing conclusions about a single population characteristic.

Related terms

Hypothesis Testing: The process of using statistical analysis to determine whether a hypothesis about a parameter of a population is likely to be true or false.

Confidence Interval: A range of values that is likely to contain an unknown population parameter, with a specified level of confidence.

Standard Error: The standard deviation of the sampling distribution of a statistic, which is used to quantify the uncertainty in the estimate of a population parameter.