Statistics Homework on Hypothesis Testing
1. The Umpa Loompas have been consuming large quantities of “Jacked Up”, which
is a performance enhancing supplement. Their employer Willy is conducting
workplace testing to ensure that the Umpa Loompas are consuming the optimal
quantity of 500 milligrams. A proper amount of Jacked Up will improve
workplace productivity, but too much will create angry loompas that do
unspeakable things to the candy. Willy has noticed both an increasing amount of
sloth by some loompas and anger by others. He doesn’t believe that the loompas
are consuming the optimal quantity. He conducts a test of 75 Loompas and finds
that they consumed 530 milligrams of Jacked Up on average. The standard
deviation of the population was 100. The sample standard deviation was 85.
Given the nature of the accusations, Willy wants to be 99% confident that he does
not make a type I error.
A. What are your null and alternative hypotheses?
B. Are you using a one or two tailed test (if one tailed, which tail?)
C. What is the test statistic?
D. What is your critical value(s)?
E. What is your p-value?
F. Do you reject the null hypothesis? Explain in terms of the test statistic
method and p-value method.
G. Change the level of significance to five percent. Did your test statistic
change? Did your critical value change?
2. White Goodman is owner of Globo-gym. He engages on a marketing campaign that his
members are better than you because his members lose an average of at least 25 pounds.
The owner of Average Joe’s Gym believes this assertion is false advertising and samples
50 Globo-gym members. He finds that they have lost an average of 23.5 pounds with a
population standard deviation of 7. He only wants a five percent chance of a type I error.
A. What are your null and alternative hypotheses?
B. Are you using a one or two tailed test (if one tailed, which tail?)
C. What is the test statistic?
D. What is your critical value(s)?
E. What is your p-value?
F. Do you reject the null hypothesis? Explain in terms of the test statistic
method and p-value method.
3. You take a sample of 25 angry llamas to see how far they can spit. The angry llama
preservation club contends they spit an average of at least 36 inches. Your sample
indicates that they spit an average of 34 inches with a sample standard deviation of 6
inches. You select a 10 percent level of significance.
A. What are your null and alternative hypotheses?
B. Are you using a one or two tailed test (if one tailed, which tail?)
C. What is the test statistic?
D. What is your critical value(s)?
E. What is your p-value?
F. Do you reject the null hypothesis? Explain in terms of the test statistic
method and p-value method.
4. Make the problem above a two tailed test (i.e. the angry llamas spit exactly 36 inches)
What is are your new critical values?
What is your new p-value?
Do you reject the null hypothesis now?