Assignment: - Hypothesis Testing and Confidence Intervals

Problem 1: The Jury Trial Analogy

Sometimes, the outcome of a jury trial defies the "commonsense" expectations of the general public. Such a verdict is more acceptable if we understand that the jury trial of an accused murderer is analogous to the statistical hypothesis-testing process. The null-hypothesis in a jury trial is that the accused is innocent. (The status-quo hypothesis in the U.S. system of justice is innocence, which is assumed to be true until proven beyond a reasonable doubt.) The alternative hypothesis is guilt, which is accepted only when sufficient evidence exists to establish its truth.  If the vote of the jury is unanimous in favor of guilt, the null hypothesis of innocence is rejected and the court concluded that the accused murderer is guilty. Any vote other than a unanimous one for guilt results in a "not guilty" verdict. The court never declares the accused "innocent". A "not guilty" verdict implies that the court could not find the defendant guilty beyond a reasonable doubt.

The Jury Trial Problem will be discussed and submitted in Assignment 6 part 2 (Discussion) and part 3 (Summary)

Problem 2: Inference application - individual write-up (18 points total)

Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The mazes are classified according to difficulty, as measured by the mean length of time it takes to find the food at the end. One researcher needs a maze that will take rats an average of one minute to solve. He tests one maze on 18 rats. Is there evidence that this maze is "too easy" or "too difficult" (implying taking something other than one minute to solve, on average)? The times to complete the maze (in seconds) for the 18 rats are given in the MAZE data set on Canvas and in the ST 351 online class folder on the k drive. Suppose the population standard deviation ( σ X ), is 2 seconds.

Type answers only to the following questions in a separate document. Make sure to number your answers in the order presented below. Submit the document with your answers only.

1. State the null and alternative hypotheses in statistical notation and in words.

2. Which hypothesis test is the most appropriate to use? Why?

3. Several conditions must be met for conclusions from this hypothesis test to be valid to the population of interest. Answer the following questions regarding these conditions:

a] Explain why a sample needs to be representative of a population when performing a hypothesis test or constructing a confidence interval.

b] Give one reason why the time to complete this maze of these 18 rats are representative of the time to complete this maze for all rats that may do this maze. Also, give one reason why the times of these 18 rats may not be representative of times for all rats that do this maze.

c] Part of having a "representative sample" is having observations that are independent of each other. In the context of this problem, explain what it means to have "independent observations". Do you feel that the observations are independent? Explain.

d] Do you believe the distribution of sample means is normal in this problem? Explain. (Hint: you should support your answer with a graph and an explanation of how you are using that graph to answer this question.)

4. Use Minitab to perform the hypothesis test. Report the test-statistic and p-value, but do NOT include the Minitab output.

5. State a conclusion in the context of the problem.

6. Report AND interpret a 95% confidence interval for the mean time to complete this maze for all rats that may do this maze.