Perform hypothesis testing on one variable’s data. (Choose either the intrinsic or extrinsic column.) Perform a t-test by formulating a null and an alternative statement, choosing an acceptable significance value, determining the appropriate critical value, selecting the test statistic and determining its value from the sample data, comparing the observed value to the critical value obtained and determining whether to reject or fail to reject the null hypothesis
Have you been given some data upon which to perform the hypothesis testing procedure? If so, we'll need to see it too in order to help.
To perform hypothesis testing on one variable's data using a t-test, you need to follow these steps:
1. Formulate the null and alternative hypotheses:
- Null hypothesis (H0): There is no significant difference between the mean of the variable and a given value.
- Alternative hypothesis (Ha): There is a significant difference between the mean of the variable and a given value.
2. Choose an acceptable significance level (alpha):
- The significance level, commonly denoted as alpha (α), determines the probability of rejecting the null hypothesis when it is true. Typical values for alpha are 0.05 (5%) or 0.01 (1%).
3. Determine the appropriate critical value:
- The critical value is based on the chosen significance level and the distribution of the test statistic. For a t-test, you would refer to a t-table or use statistical software to find the critical value.
4. Select the test statistic and determine its value from the sample data:
- For a t-test, the test statistic is usually the t-value. The t-value is calculated based on the sample mean, sample standard deviation, sample size (or degrees of freedom), and the hypothesized population mean.
5. Compare the observed value to the critical value obtained:
- Compare the absolute value of the calculated t-value to the critical value. If the calculated t-value exceeds the critical value, you reject the null hypothesis. Otherwise, if the calculated t-value is less than or equal to the critical value, you fail to reject the null hypothesis.
6. Determine whether to reject or fail to reject the null hypothesis:
- If the observed value (calculated t-value) exceeds the critical value, then you reject the null hypothesis. This means that there is evidence to suggest a significant difference between the mean of the variable and the given value.
- If the observed value is less than or equal to the critical value, you fail to reject the null hypothesis. This means that there is not enough evidence to conclude a significant difference between the mean of the variable and the given value.
It's important to note that the specific formulas and calculations for the t-test depend on whether you are performing a one-sample t-test, independent samples t-test, or paired samples t-test. The steps outlined above provide a general framework for hypothesis testing using a t-test.