In a related study, Zwerg, when given two choices, successfully chose the object indicated by a “marker” 26 out of 48 times. Does this result show that Zwerg can correctly follow this type of direction (“placing a marker”) by an experimenter more than 50% of the time?
a. Define the parameter of interest in the context of the study and assign a symbol to it.
b. State the null hypothesis and the alternative hypothesis using the symbol defined in part (a).
c. What is the observed proportion of times Zwerg picked the correct object? What symbol should you use to represent this value?
d. Suppose that you were to generate the null distribution of the sample proportion of correct answers, that is, the distribution of possible values of sample proportion of correct identifications if Zwerg always guesses. Where would you anticipate this distribution would center? Also, do you anticipate the SD of the null distribution to be negative, positive, or 0? Why?
e. Use an applet to generate the null distribution of sample proportion of correct answers and use it to determine the standardized statistic.
f. Interpret the standardized statistic in the context of the study.
g. Based on the standardized statistic, state the conclusion that you would draw about the research question of whether Zwerg does better than randomly guess when the cue is that the experimenter places a marker in front of the correct object.