Question

1.3.22 Choosing numbers Use the following information to answer the next four questions. One of the authors read somewhere that it’s been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose “3” more than would be expected by random chance. To investigate this, she collected data in her class. Here is the table of responses from her students:

chose 1	chose 2	chose 3	chose 4
10	4	14	5

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 students chose the number 3? 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. Interpret the standardized statistic in the context of the study. (Hint: You need to talk about the value of your observed statistic in terms of standard deviations assuming ______ is true.)

g. Based on the standardized statistic, state the conclusion that you would draw about the research question of whether students tend to have a genuine preference for the number 3 when given the choices 1, 2, 3, and 4.

Answer 1