Research experiments sometimes involve testing the agility of rats on a rotating cylinder task. The task has an endurance component where a fixed rotation cycle is set, and rats are measured by the length of time they can remain on the cylinder before landing in a cushioned chamber below. One graduate student is told that healthy rats of a certain strain typically remain on the cylinder an average of about fifty seconds. He performs the rotating cylinder task on several Long Evans rats, collecting the data (in seconds) as shown below: 38.4 44.6 52.5 48.0 62.8 53.9 50.4 35.0 45.8 50.1 55.1 65.6 55.5 49.5 50.9 44.3 75.8 47.9 76.2 46.2 56.3 Is there evidence that the mean endurance time for this task is 50 seconds? Use alpha α = 0.05. determine if there is sufficient evidence to suggest that the mean endurance time for this task is 50 seconds. For your handwork, follow hypothesis testing. Specifically, your answer should include: State the statistical hypotheses (using the appropriate notation). Indicate whether the alternative hypothesis is non-directional or directional (and how you know). Set the decision rules, which will include: o State alpha Compute the degrees of freedom o Providing the critical value for the test statistic o Sketch the curve and label the rejection region o State the decision rules o Sample mean o Standard error of the mean o Population mean o Test statistic Calculate the test statistic. You can do this by using the values of the sample mean and standard error of the mean (you do not have to calculate the sample mean and standard error of the mean from the raw data). Draw a conclusion (state whether H0 is rejected or not and why you made this decision). Interpret the result
textbook practise question I am stumped on when studying for how to do statistical hypothesis testing:
Research experiments sometimes involve testing the agility of rats on a rotating cylinder task. The task has an endurance component where a fixed rotation cycle is set, and rats are measured by the length of time they can remain on the cylinder before landing in a cushioned chamber below. One graduate student is told that healthy rats of a certain strain typically remain on the cylinder an average of about fifty seconds. He performs the rotating cylinder task on several Long Evans rats, collecting the data (in seconds) as shown below:
38.4 44.6 52.5 48.0 62.8 53.9 50.4 35.0 45.8 50.1 55.1 65.6 55.5 49.5 50.9 44.3 75.8 47.9 76.2 46.2 56.3
Is there evidence that the
Use alpha α = 0.05.
determine if there is sufficient evidence to suggest that the mean endurance time for this task is 50 seconds. For your handwork, follow hypothesis testing. Specifically, your answer should include:
State the statistical hypotheses (using the appropriate notation).
Indicate whether the alternative hypothesis is non-directional or directional (and how you know).
Set the decision rules, which will include:
o State alpha
Compute the degrees of freedom
o Providing the critical value for the test statistic
o Sketch the curve and label the rejection region
o State the decision rules
o Sample mean o Standard error of the mean
o Population mean
o Test statistic
Calculate the test statistic. You can do this by using the values of the sample mean and standard error of the mean (you do not have to calculate the sample mean and standard error of the mean from the raw data).
Draw a conclusion (state whether H0 is rejected or not and why you made this decision).
Interpret the result
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