Inferential statistics involves forming conclusions about a population parameter. We do so by constructing confidence intervals and testing claims about a population mean and other statistics. Typically, these methods deal with a sample from one population. We can extend the methods to situations involving two populations (and there are many such applications). This deliverable looks at two scenarios.
Your focus is on hypothesis tests and confidence intervals for two populations using two samples, some of which are independent and some of which are dependent. These concepts are an extension of hypothesis testing and confidence intervals which use statistics from one sample to make conclusions about population parameters.
Your research and analysis should be presented on the spreadsheet provided.
Instructions – Read First
Instructions: The following worksheets describe two problems – the first problem is for independent samples and the second problem is for dependent samples. Your job is to demonstrate the solution to each scenario by showing how to work through each problem in detail. You are expected to explain all of the steps in your own words.
Independent Samples
| Low Lead Level | High Lead Level | |||
| n1 | 60 | n2 | 20 | |
| 91.44 | 82.7 | |||
| s1 | 17.45 | s2 | 9.68 | |
| Critical Value: | ||||
| Test Statistic: | ||||
| p-value: |
1. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.
2. Calculate the critical value, the test statistic, and p-value. Show calculations below.
3. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.
Independent Samples A researcher conducted a test to learn the effect of lead levels in human bodies. He collected the IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The summary of finding is listed below. Use a 0.05 significance level to test the claim that the mean IQ score of people with low lead levels is higher than the mean IQ score of people with high lead levels. We do not know the values of the population standard deviations.
Dependent Samples
| Days of Release/Book | Phoenix | Prince | |
| 1 | 44.3 | 58.2 | |
| 2 | 18.4 | 22.0 | |
| 3 | 25.8 | 28.6 | |
| 4 | 28.3 | 29.2 | |
| 5 | 22.0 | 21.8 | |
| 6 | 9.9 | 10.7 | |
| 7 | 9.3 | 9.4 | |
| 8 | 8.4 | 7.5 | |
| 9 | 7.6 | 6.9 | |
| 10 | 10.2 | 9.2 | |
| Critical Value: | |||
| Test Statistic: | |||
| p-value: |
4. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.
5. Calculate the critical value, the test statistic, and p-value. Show calculations below.
6. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.
Dependent Samples The Harry Potter books and movies made a lot of money. A fan wanted to learn which of his favorite movies made more money. He collected the amounts grossed in millions during the first few days of releases of the movies Harry Potter and the Half-Blood Prince and Harry Potter and the Order of the Phoenix. Use a 0.05 significance level to test his claim that the Prince movie did better at the box office. Use the p-value method to determine whether or not to reject the null hypothesis and state your conclusion.
