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Signs you're adulting
Conducted by OnePoll on behalf of Avocado Green Brands, a recent survey of 2,000 Americans
delved into the different actions that have helped respondents to feel like an adult. Topping the list
was living on their own (30%) for the first time, followed by buying a house (28%) and getting
married (27%).
a) If we define a "success" as thinking that buying a house makes one feel like an adult, how many
successes would we find in this sample of 2000 Americans?
Give an integer
answer.
b) Construct a 98% confidence interval to estimate the proportion of all Americans who think that
living on their own makes someone feel like an adult, assuming a sample size of 2000 and the
statistics given by One Poll. Give each of the interval endpoints as a percent, rounded to one
decimal places. (
%,
%)

Respuesta :

MrRoyal

The 98% confidence interval of the proportion of all Americans who think that living on their own makes someone feels like an adult is (29.0%, 31.0%)

The number of success

The given parameters are:

  • Sample size, n = 2000
  • Probability of success, p =28%

The number of success is then calculated as;

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 2000 * 28\%[/tex]

Evaluate

[tex]\bar x = 560[/tex]

Hence, 560 successes would be found in the sample of 2000 Americans

The 98% confidence interval

The proportion that lives on their own is:

p = 30%

The z-score for 98% confidence interval is

z = 2.326

The confidence interval is calculated as:

[tex]CI = \bar p \pm z * \sqrt{\frac{\bar p(1 - \bar p)}{ n}[/tex]

So, we have:

[tex]CI = 30\% \pm 2.326 * \sqrt{\frac{30\%(1 - 30\%)}{2000}[/tex]

Evaluate

[tex]CI = 30\% \pm 1\%[/tex]

Expand

CI = (30% - 1%, 30% + 1%)

Evaluate

CI = (29%, 31%)

Hence, the 98% confidence interval is (29.0%, 31.0%)

Read more about confidence interval at:

https://brainly.com/question/24131141

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