10.3: t-tests about a Population mean: SD Unknown Flashcards
When is a t-test about a population mean used?
A t-test about a population mean is used when the population standard deviation (σ) is unknown and the sample size is small (n < 30).
What is a t-test?
A t-test is a statistical test used to determine if there is a significant difference between the means of two groups, which may be related in certain features.
How is the t-test statistic calculated when the population standard deviation is unknown?
t = (x̄ - μ₀) / (s / √n),
where x̄ is the sample mean, μ₀ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
What are degrees of freedom in a t-test?
Degrees of freedom (df) in a t-test are calculated as n - 1, where n is the sample size.
What assumptions must be met for a t-test?
The sample must be from a normally distributed population or have a large size (n ≥ 30).
What does the null hypothesis state in a t-test?
The null hypothesis (H₀) states that the true mean is equal to the hypothesized value, written as H₀: μ = μ₀.
How is the critical value used in a t-test?
If the absolute value of the calculated t is greater than the critical t value from the t distribution table, the null hypothesis is rejected.
What is a p-value in a t-test?
The p-value represents the probability of obtaining a result at least as extreme as the observed one, assuming that the null hypothesis is true.
How is the p-value used in hypothesis testing?
If the p-value is less than the chosen alpha level (α), the null hypothesis is rejected; otherwise, it is not rejected.
What is a two-tailed t-test?
A two-tailed t-test tests the possibility of a relationship in both directions, meaning the actual mean could be either less than or greater than the hypothesized mean.
When is a one-tailed t-test used?
A one-tailed t-test is used when the research hypothesis states that the parameter has either increased or decreased, but not both.
What should be done if the population standard deviation is unknown for hypothesis testing?
If the population standard deviation is unknown, a t-test should be used for hypothesis testing instead of a z-test.
Can the t-test be used for large sample sizes even if the population is not normally distributed?
Yes, the t-test is approximately valid for large sample sizes (at least 30) even if the population is not normally distributed.
Under what condition should the null hypothesis be retained in a t-test?
The null hypothesis should not be rejected if the absolute value of the t-test statistic is less than the critical value from the t-distribution table.
How is the p-value calculated in a two-tailed t-test?
The p-value is the area under the t-distribution curve that corresponds to the test statistic’s calculated value.
