Statistics One-Sample t-Test

What is the first step in carrying out a significance test for a single mean?

What indicates that a sample can be analyzed using the t-test when the population is not normal?

Which of the following is NOT a form of the null and alternative hypotheses in a one-sample t test?

In what scenario is a random sample of any size acceptable when conducting a t-test?

Which step comes after verifying conditions in hypothesis testing?

What type of hypothesis is being tested when H0: µ = µ0 versus Ha: µ < µ0?

When conducting a t-test, what is essential to ensure the validity of the results?

Which conclusion can be drawn if the P-value is lower than the level of significance?

One-Sample t-Test for Mean

The one-sample t-test is used when the population standard deviation (σ) is unknown
The test follows four steps: state hypotheses, check conditions, calculate the test statistic, and interpret the p-value and draw a conclusion.

Steps in One-Sample t-Test

Step 1: State the null and alternative hypotheses, and the level of significance (α).
- Null hypothesis (H0): µ = µ0 (population mean is equal to a specific value)
- Alternative hypothesis (Ha):
  - µ ≠ µ0 (two-sided): The population mean is different from the specific value
  - µ < µ0 (one-sided): The population mean is less than the specific value
  - µ > µ0 (one-sided): The population mean is greater than the specific value
Step 2a: Verify the necessary conditions before calculating the test statistic:
- The data must be a random sample.
- Situation 1: If the population is normally distributed, a random sample of any size is acceptable.
- Situation 2: If the population is not normal and exhibits skewness or outliers, a large random sample (n ≥ 40) is required.
  - To determine normality, visually inspect the data using a histogram or dot plot.
  - A large sample size helps to ensure that the distribution of the sample mean is approximately normal.

This quiz covers the one-sample t-test for mean, focusing on its application when the population standard deviation is unknown. Learn the essential four steps: state hypotheses, check conditions, calculate the test statistic, and interpret results. Test your understanding of these statistical concepts and procedures.