Psychology experiments sometimes involve testing the ability of rats to navigate

Question

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 ( X ), is 2 seconds.

1. State the null and alternative hypotheses in statistical notation and in words. (3 points)

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

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. (1 point)

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. (2 points)

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. (1 point)

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.) (2 points)

4. State a conclusion in the context of the problem. (3 points)

5. Report AND interpret a 95% confidence interval for the mean time to complete this maze for all rats that may do this maze. (3 points)

Explanation / Answer

1) Let be finishing time in minutes, we want to know if =!1

Hypothesis test:

H0 : =1
Ha : =!1

This is a two tailed test

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