Suppose that you wanted to investigate whether people tend to pick a “big” number (3 or 4) rather than a “small” number (1 or 2).
a. In this context, define the parameter of interest and assign a symbol to it.
b. State the null hypothesis and the alternative hypothesis using the symbol defi ned in part (a).
c. Recall that, of 33 students, 19 picked a “big” number (that is, 3 or 4). What is the observed proportion of times students picked a “big” number? What symbol should you use to represent this value?
d. Use an applet to generate the null distribution of the proportion of “successes.” Report the mean and SD of this null distribution.
e. Determine the standardized statistic for the observed sample proportion of “successes.”
f. Based on the standardized statistic, state the conclusion that you would draw about the research question of whether people tend to pick a “big” number.