Question

in chapter 18, you are introduced to the idea of a sampling distribution. the purpose of the next few questions is to help you better understand what a sampling distribution is and how we can use what is known about sampling distributions to answer different kinds of questions.
when you started college, were you undecided about what major to pursue? suppose it turns out that in the population of all college students, 41% begin college feeling uncertain about what major to pursue.

1. imagine that you survey a random sample of ( n = 50 ) college students and find that 22 of these students were undecided about what major to pursue when they started college.

what will your sample proportion, or ( hat{p} ), be? please calculate this number below.

Explanation:

Step1: Recall the formula for sample proportion

The formula for sample proportion $\hat{p}$ is $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes in the sample and $n$ is the sample size.

Step2: Identify the values of $x$ and $n$

Here, $x = 22$ (the number of undecided students in the sample) and $n=50$ (the sample size).

Step3: Calculate the sample proportion

Substitute the values into the formula: $\hat{p}=\frac{22}{50}= 0.44$.

Answer:

The sample proportion $\hat{p}$ is $0.44$.