Question

identify the individual, variable, random variable x and the random variable $widehat{p}$ in the context of this problem.
the individual is select an answer
the variable is select an answer
the wording in x = select an answer
the wording in $widehat{p}$ = select an answer
b) can we say that the sampling distribution of $widehat{p}$ is approximately normal?

Explanation:

• Individual: In a statistical study, an individual is the single - entity being observed. Here, it is a randomly selected college student.
• Variable: A variable is a characteristic of an individual. Whether or not a randomly selected college student is left - handed is a variable as it can take two values (yes or no).
• Random variable X: Usually, X represents a count or a measurement. The number of 212 randomly selected college students that are left - handed is a random variable X as it is a count.
• Random variable $\hat{p}$: $\hat{p}$ represents a sample proportion. The proportion of 212 randomly selected college students that are left - handed is $\hat{p}$.

For part (b), to determine if the sampling distribution of $\hat{p}$ is approximately normal, we use the following rules: For a sampling distribution of a sample proportion $\hat{p}$ to be approximately normal, we need $np\geq5$ and $n(1 - p)\geq5$, where $n$ is the sample size and $p$ is the population proportion. If we assume a reasonable population proportion of left - handed college students (say $p = 0.11$ as given in one of the options) and $n=212$, then $np=212\times0.11 = 23.32\geq5$ and $n(1 - p)=212\times(1 - 0.11)=212\times0.89 = 188.68\geq5$. So, the sampling distribution of $\hat{p}$ is approximately normal.

Answer:

• The individual: a randomly selected college student
• The variable: whether or not a randomly selected college student is left - handed
• $X$: the number of 212 randomly selected college students that are left - handed
• $\hat{p}$: the proportion of 212 randomly selected college students that are left - handed
• b) Yes, the sampling distribution of $\hat{p}$ is approximately normal.