Answer:
see explanation :), It is important to note that the specific steps and procedures may vary depending on the specific context, type of data, and test assumptions. It is recommended to consult appropriate statistical resources or consult with a statistician for the accurate application of the z-test or t-test in a given scenario.
Explanation:
Determining the decision and conclusion using a z-test and t-test typically involves the following steps:
1. Formulate the null and alternative hypotheses: Start by stating the null hypothesis (H₀) and the alternative hypothesis (H₁) based on the research question or problem at hand.
2. Select the appropriate test: Determine whether a z-test or t-test is appropriate based on the characteristics of the data and the population under consideration. The choice depends on factors such as sample size, population standard deviation availability, and the assumptions of the test.
3. Set the significance level (α): Determine the desired level of significance or the probability of rejecting the null hypothesis when it is true. Commonly used values for α include 0.05 or 0.01.
4. Calculate the test statistic: For a z-test, calculate the z-score by subtracting the population mean from the sample mean, dividing by the standard deviation, and considering the sample size. For a t-test, calculate the t-value using the appropriate formula based on the type of t-test (e.g., independent samples, paired samples) and the sample data.
5. Determine the critical value: Based on the chosen significance level and the type of test, identify the critical value from the corresponding distribution table (e.g., z-table or t-table).
6. Compare the test statistic and critical value: Compare the calculated test statistic to the critical value. If the test statistic falls in the rejection region (i.e., it is greater than or less than the critical value), then reject the null hypothesis. If the test statistic does not fall in the rejection region, fail to reject the null hypothesis.
7. State the decision: Based on the comparison in the previous step, make a decision regarding the null hypothesis. If the null hypothesis is rejected, it suggests evidence in favor of the alternative hypothesis. If the null hypothesis is not rejected, there is not enough evidence to support the alternative hypothesis.
8. Draw conclusions: Based on the decision, draw conclusions about the research question or problem. Summarize the findings and discuss the implications based on the statistical analysis.