Assignment:
A reminder about Academic Integrity from the syllabus:
Violations of the Academic Integrity Policy (a.k.a. cheating in its various forms) will be severely punished. The minimum penalty is a grade of zero on the assignment in question, but it can go up to expulsion from the university. If you have not done so yet, please familiarize yourself with the Academic Integrity Policy (available online at https://www.wpunj.edu/dotAsset/230122.pdf). All parts of that Policy are relevant and important, but for the online setting of the class, I especially would like to stress sections II.B. (on plagiarism) and II.C. (on collusion). Please make sure that you truly understand what all parts of the policy mean. To name a few examples, working together with another student on an assignment, getting help on an assignment from someone else (e.g., a tutor), and copying another student's work are all violations of the Academic Integrity Policy.
Question 1
Suppose that you want to test the claim that the mean weight of the giant Pacific octopus is 35 pounds or more. You collect a sample of 90 octopuses and find that the mean weight in the sample is 34 pounds. The standard deviation is 4 pounds.
Part (a)
Given that the average in the sample is less than what is claimed in the null hypothesis, is it still necessary to carry out a hypothesis test to test the claim? Please answer "yes" or "no," then explain your answer.
Part (b)
Using a level of significance α of 0.01, test the null hypothesis H0: µ≥35 using the 6-step procedure.
Part (c)
Using a level of significance α of 0.01, test the null hypothesis H0: µ≥35 using the p-value.
(Reminder: Your decision whether to reject or not reject H0 will be the same with the 6-step procedure and the p-value, but you must show how you arrive at that conclusion.)
Question 2
Suppose that someone claims that adult male bottlenose dolphins, on average, weigh 700 pounds or less. To test that claim, you catch, weigh, and release 87 adult male bottlenose dolphins. You find that the mean weight is 715 pounds. The standard deviation is 84 pounds.
Part (a)
State two levels of significance (literally; you must write down two values) at which the null hypothesis is rejected.
Part (b)
State two levels of significance (literally; you must write down two values) at which the null hypothesis is not rejected.
Question 3
Part (a)
The following information is given:
- The sample consists of 119 cars driving down Hamburg Turnpike. Their mean speed is 42 miles per hour.
- α = 0.05
- The test statistic has a standard normal distribution (if H0 is true).
If it is possible to determine the critical value(s) based on this information, determine it/them. If it is not possible, explain why it is not possible.
Part (b)
Part (b) is independent from Part (a), i.e., do not use information from Part (a) to answer Part (b).
The following information is given:
- α = 0.10
- The null hypothesis is that the mean thickness of a certain kind of wire is 0.5 millimeters.
- The test statistic has a standard normal distribution (if H0 is true).
If it is possible to determine the critical value(s) based on this information, determine it/them. If it is not possible, explain why it is not possible.
Question 4
Would it make sense to carry out a hypothesis test to test a claim about a sample mean? Why or why not?
Hint: It may help you to answer this question to think about why we carry out a hypothesis test to test a claim about a population mean.