USA today provided a “snapshot” illustrating poll results from 21,944 subjects. The illustration showed that 43% answered “yes” to this question : ” Would you rather have a boring job than no job?” The margin of error was given as plus and minus 1 percentage point.
1. Describe what is meant by the statement that the “the margin of error is plus and minus 1 percentage point”.
2. Also, we are given that 43% of 21,944 people polled answered “yes”. Given that 43% is the best estimate of the population percentage, why would we need a confidence interval?
Part II:
Find an article on public opinion survey data Links to an external site. based on your interest. Each of these studies report the percentage(s) of US adults agreeing with the given topic’s primary question(s). This percentage is the “sample proportion of success = phat”. Make sure to check that they report the sample size used in “How we did this” section (in rare instances, the sample size is not reported). Now use the sample proportion of success and the sample size to calculate a 95% confidence interval for the true population proportion. For the purpose of this discussion provide the following:
In 100 words share the topic you have chosen and the motivation behind choosing this topic. Include the parameter of interest. Share the link of the survey article.
Clearly show the calculation of the confidence interval by indicating the value of n, p-hat, and z for a 95% confidence interval. Check conditions.
Explain what the interval means in context.
2 Peer Responses due by Sunday, 7/14. The responses should thoughtfully address the topic being discussed in the article ( Some points you could talk about are : your personal motivation to respond to the topic; sampling method used and how it informs constructing a confidence interval requirements; what other questions could have added value to the topic; etc), the calculation of the interval and writing the interpretation.
(See an example below)
Confidence Intervals for Public Opinion on How Teens and Parents Approach Screen TimeLinks to an external site.
This Pew Research Center survey aimed to gather insight from US parents and their teens to better understand their experiences with screen time. I am a parent with a teen kid so I get to see kids these age at social gatherings, school events, playdates etc. and have noticed how quickly screen time and social media populated the lives of kids since when my oldest (who is in junior year of college) was in middle school. The study does a good job in gathering screen time use from both teens and parents alike. Interestingly enough, parents also tend to spend a lot of time on their phones and the trends are interesting when disaggregated by income and race and ethnicity. I am able to relate to the questions addressed in this study was happy to share it with my teen. In this example, I will focus on “Do parents think they spend too much time on their phone?”
Parameter of Interest: % of US parents of teens ages 13-17 who say the amount of time they spend on their smartphone is too much
Sample Proportion (p-hat): According to the survey, 47% of parents believe they spend too much time on their smart phones. This is our p-hat.
Confidence Interval (CI): I will find the 95% confidence interval for the true proportion of all US parents of teens ages 13-17 who say the amount of time they spend on their smartphone is too much.
n = sample size = 1,453
z-value for a 95% confidence level = 1.96
Checking Conditions:
Randomization condition: is met because participants were identified using a random sample of residential addresses.
10% condition: is met because the sample of 1,453 parents of teens ages 13-17 is less that all parents of teens ages 13-17 in the population
Success/Failure condition: is met because there are
𝑛
∗
𝑝
^
=
1453
∗
0.47
=
682.91
≥
10
successes and
𝑛
∗
𝑞
^
=
1453
∗
0.53
=
770.09
≥
10
failures
I will use the following formula:
𝑝
^
±
1.96
𝑝
^
𝑞
^
𝑛
0.47
±
1.96
0.47
∗
0.53
1453
0.47
±
0.0257
(0.4443, 0.4957)
Interpretation: We are 95% confident that the true proportion of all US parents of teens ages 13-17 who say the amount of time they spend on their smartphone is too much falls between 44.4% and 49.6%.
As alarming as the dependence on smart phones may have become, it is clear that it is affecting people across all age groups. As parents and adults we should have a better understanding of habits that can send a wrong message to our teens and youth. Setting good examples is one of our responsibility that should not be ignored.
