1. Manny the Monkey was given an option of three different but identical bunches of bananas to choose from. One of the three bunches was predetermined to be the “winning” bunch by the researchers. This study was double-blind, so neither Manny nor his handler knew which bunch was the winning bunch. Manny correctly chose the “winning” bunch 15 out of 30 times he completed the experiment.
Is Manny the Monkey is “psychic”? Specifically, does this sample provide evidence that Manny was correct more often than if he was just guessing? Test using a 5% significance level.
(a) State hypotheses for the test.
(b) Show confirmation that the CLT applies.
(c) Calculate the test statistic for the sample.
(d) Calculate a p-value for the sample. For full credit, you MUST write down what calculator command you used to find a p-value and/or draw a picture of the appropriate distribution displaying how your p-value was found.
(e) What is your conclusion? Be sure to state it in a complete sentence, in context.
2. Nineteen mice were randomly separated into one group with darkness at night and one group with a dim light on at night. Although the mice ate the same amounts and exercised the same, the sample mice with the light at night gained more weight. The body mass gain, in grams, for the mice in the two groups after 4 weeks is given below.
DimLight 3 5 6 6 7 8 9 10 11 13
NoLight 3,4 5 6 6 6 7 8 8
We wish to estimate the difference in mean body mass gain when comparing dim light at night to complete darkness.
(a) Identify the parameter of interest using appropriate notation, and define in words what the notation(s) represent.
(b) Explain why the CLT is appropriate to use for this sample.
(c) Create a 99% confidence interval, showing all work and calculations. Interpret your interval in context.