Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
The confidence interval is 0.028, 0.872
Given
862 of 1013 randomly selected adults wear seat belts.
The 95% confidence interval for the proportion of adults who always wear seat belts.
What is confidence interval?
A Confidence Interval is defined as a range of values we are sure our true value lies within it.
What is 95% confidence interval?
A 95% confidence interval is defined as that if we take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value.
= 862/1013 = 0.85
At a 95% confidence interval ,the critical value is [tex]z_{0.025} = 1.96[/tex]
The 95% confidence interval for proportion is
[tex]\widehat p +/- z0.025 * sqrt(\widehat p * (1 - \widehat p)/n)[/tex]
[tex]= 0.85 +/- 1.96 * sqrt(0.85 * (1 - 0.85)/1013)[/tex]
[tex]= 0.85 +/- 0.022[/tex]
= 0.028, 0.872
The sample should use at least 10 successes and 10 failures.
[tex]n * \widehat p = 1013 * 0.85 = 861 > 10[/tex]
[tex]n * (1 - \widehat p) = 1013 * 0.15 = 152 > 10[/tex]
As the sample size is larger, we can use an approximate formula for the standard error.
Learn more on Confidence intervals here:
https://brainly.com/question/8961482
#SPJ4
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.