10B Coreq

In the next preview assignment and in the next class, you will need to identify the essential components of a confidence interval and interpret a confidence interval for a population proportion in context. This corequisite support activity will review important concepts, notation, and terminology associated with populations and samples, as well as the connections between them.
Recalling Connections Between Populations and Samples

Question 1

In In-Class Activity 9.A, we learned about the differences between a population and a sample. In your own words, describe the differences between a population and a sample.

Question 2

In multiple prior lessons, we learned there are characteristics and calculations that  relate to and/or describe a population and those that relate to and/or describe a  sample. Fill in the blank:

  1. A ___________ is a characteristic of a population of interest.
  2. A ___________ is a characteristic of a sample or subgroup of interest.

Question 3

For each of the following scenarios, determine whether the characteristic is a  parameter or a statistic.

  1. A school administer needs to identify the proportion of all students who are  registered for at least nine credits in the Spring semester. She uses the  school’s registration system to identify all students who are registered for the  semester and then calculates the proportion of those who are registered for  at least nine credits.
    The proportion of all students who are registered for at least nine credits is  an example of a ____________ [parameter or statistic] because it describes  a _____________ [population or sample].
  2. A researcher would like to estimate the true proportion of procedures at a  hospital that involved a complication. The researcher randomly selects 200  procedures from the past year, identifies whether the procedures involved complications, and then calculates the proportion.
    The proportion of procedures that involved a complication—out of the 200  randomly selected—is an example of a ____________ [parameter or statistic] because it describes a _____________ [population or sample].
  3. A survey of 6,870 college students found that approximately 65%, or 4,466  of the students surveyed, ordered take-out or delivery at least once in the  last seven days.
    The calculated percentage, 65%, is a ____________ [parameter or statistic]  because it describes a _____________ [population or sample].

In Lesson 9 and In-Class Activity 10.A, we learned about the connections between a  population and the sampling distribution of a sample proportion from that population.  That is, when taking many random samples of size [latex]n[/latex] from a population distribution with  proportion [latex]p[/latex], the mean of the distribution of sample proportions is [latex]p[/latex] and the standard deviation of the distribution of sample proportions is [latex]\sqrt{\frac{p(1-p)}{n}}[/latex].

However, we rarely (if ever) know the true value of the population proportion. So  instead, we can estimate the mean and standard deviation of the sampling distribution  by the following:

Estimate for the mean of sample proportions = [latex]\hat{p}[/latex] = sample proportion

Estimate for the standard deviation of sample proportions (e.g., standard error) = [latex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/latex]

 

Question 4

Suppose we took a random sample of 288 college students at a particular college  and found that 176 were scheduled for at least nine credits in the upcoming  semester.

  1. Calculate the sample proportion or point-estimate, [latex]\hat{p}[/latex].
  2. Interpret your value for [latex]\hat{p}[/latex]. What does this value suggest in the context of this  situation?
  3. Calculate the standard error of the sample proportion using the formula [latex]SE= \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/latex] and the point-estimate you calculated previously.
  4. Interpret your value for the standard error. What does this value suggest in the context of this situation?

Practice

Question 5

In the 2019 National College Health Assessment, a random sample of college  students were asked, in the last 7 days, “How many servings of fruit did you eat on  average per day?” Out of the 38,466 responses, 6,125 students stated they  consumed an average of 0 servings of fruit per day.[1]

Let [latex]p[/latex] represent the proportion of all college students who reported that they  consume an average of 0 servings of fruit per day.

  1. Part A: Calculate the sample proportion or point-estimate, [latex]\hat{p}[/latex]
  2. Part B: Calculate the standard error of the sample proportions using the formula [latex]SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/latex]

Question 6

Interpret your calculations from Question 5. What are these values estimating with  respect to the given context/situation?

Question 7

Looking at the value of the standard error that you calculated in Question 5, why do  you suppose the value is so small? Explain.

 

 

  1. American College Health Association-National College Health Assessment. (2020). Undergraduate student reference group data report, Fall 2019. https://www.acha.org/NCHA/ACHA NCHA_Data/Publications_and_Reports/NCHA/Data/Reports_ACHA-NCHAIII.aspx ↵