15. Based on the information given for each of the following studies, decide
whether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected, (b) the Z score on the comparison distribution for the sample score, and(c) your conclusion. Assume that all populations are normally distributed.
We do not have access to your studies.
To determine whether to reject the null hypothesis in each of the following studies, we need to compare the sample score to the distribution of scores under the null hypothesis. Here's how you can go about it:
Step 1: Set up the null and alternative hypotheses.
- The null hypothesis (H0) typically states that there is no significant difference or relationship between variables.
- The alternative hypothesis (Ha or H1) typically states that there is a significant difference or relationship between variables.
Step 2: Determine the significance level (alpha).
- The significance level, denoted as alpha (α), is the threshold at which we will reject the null hypothesis. Commonly used values for alpha are 0.05 (5%) or 0.01 (1%), but they may vary depending on the study.
Step 3: Choose the appropriate statistical test.
- The choice of statistical test depends on the nature of the data and the research question. Some commonly used tests include t-tests, z-tests, chi-square tests, etc.
Step 4: Calculate the test statistic and p-value.
- The test statistic measures the difference between the sample and population means, proportions, or other relevant measures.
- The p-value represents the probability of obtaining a test statistic as extreme as (or more extreme than) the observed sample statistic, assuming the null hypothesis is true.
Step 5: Compare the test statistic to the critical value or p-value.
- If the test statistic exceeds the critical value (i.e., the Z-score cutoff), we reject the null hypothesis. The specific critical value depends on the chosen statistical test and alpha level.
- Alternatively, if the p-value is less than the chosen significance level (alpha), we reject the null hypothesis. A smaller p-value suggests stronger evidence against the null hypothesis.
Step 6: Interpret the results and draw a conclusion.
- Based on the comparison of the test statistic to the critical value or p-value, we can either reject or fail to reject the null hypothesis.
- If the null hypothesis is rejected, it suggests that there is significant evidence to support the alternative hypothesis.
- If the null hypothesis cannot be rejected, it suggests that there is insufficient evidence to conclude a significant difference or relationship.
Without specific details about the studies, the comparison distribution, and the sample score, it is not possible to provide the Z-score cutoffs or draw any conclusions. Please provide more information for each study, and I can guide you on how to determine whether to reject the null hypothesis.