Question

1) To test the null hypothesis in the James Bond experiment (test his claim that he can taste the difference between a Martini that is shaken and one that is stirred) you have him taste 8 shaken martinis and 8 stirred martinis, presented in a random order. How would you interpret the results of the experiment if he was correct on 0 (zero) out of 16 times?

2) An experimenter expects an effect to come out in a certain direction. Is this sufficient basis for using a one-tailed test? Why or why not?

3)Imagine an ad asking for employees of a company to volunteer for a study in which diets and eating would be discussed. The sample of people who would volunteer for such a study would not be representative of the employees of the company. This is called­___

a. Undercoverage bias       
b. Survivorship bias   
c. Self-selection bias

4) In an experiment, if subjects are sampled randomly from a population and then assigned randomly to either the experimental group or the control group, we can be sure than the treatment caused the difference in the dependent variable. (True or false?)

Please answer both, these are questions I have to know for my exam which I am struggling with. Thank you!!

Answer 1

Part 1

let p be the proportion of the observations that have been answered correctly i.e. proportion of correct answers by James Bond.

to test, $H_0 : p = 1 \ vs \ H_1 : p < 1$

We shall use the one sample Z test,

where the test statistic is given as, Z = (p - 1) / se(p)

Based on the given observation, it is very likely to state that we reject the null hypothesis as p = 0 for this case and observed Z would be much less than the critical value which is -1.9599 at 95% confidence.

Part 2

No. Use of a one tailed test depends on the objective of the experiment and what is it that we want to test. If the required test is directional, that is when we use a one-tailed test.

It is true to look for a one tailed test when an experimenter expects an effect to come out in a certain direction, but it may or may not affect our nature of the test.

Part 3

Undercoverage bias

Part 4

False. Randomization is not the only factor that enhances the analysis capability of the experiment. Replication and Local Control are also to be employed in the experimental design to ensure that the due to randomization are consistent over many cases, and local control also quantifies unknown factors that may affect the experiment and hence we may clearly find the difference in the target variable.