Explain the difference between independent samples and dependent samples

Assignment 2: Mixed Problems .
In what ways is the t distribution similar to the standard normal distribution? In what ways is the t distribution different from the standard normal distribution? How does the formula for the t test differ from the formula for the z test? (6pts)
Choose a variable. Before collecting the data, decide what a likely average might be, then complete the following: (12 pts)
Write a brief statement of purpose of the study
Define the population
State the hypotheses for the study
Select an a value
State how the sample was selected
Show the raw data
Decide which statistical test is appropriate and compute the test statistic (z or t). Why is the test appropriate?
Find the critical values(s)
State the decision
Summarize the results.
You may obtain raw data from the random number table in the appendix section of your text or from any other sources, including sources on the World Wide Web.
Explain the difference between testing a single mean and testing the difference between two means. What two assumptions must be met when one is using z test to test differences between two means? When can the sample standard deviations s1 and s2 be used in place of the population standard deviations S1 and S2 ? (6 pts)
Explain the difference between independent samples and dependent samples. Classify the following as independent or dependent samples: (6 pts)
Weights of identical twins
The effectiveness of two different brands of ibuprofen
Effect of a new training program on time taken to complete a task, measured by a “before” and “after” test
Test scores of a group of students on a math test and a biology test.
Complete the following: (30 pts)
Select a variable. Compare the mean of the variable for a sample of 30 for one group with the mean of the variable for a sample of 30 for a second group. Use a z test.
Select a variable.