Respuesta :
Answer:
The confidence interval for this proportion = (0.09, 0.13)
Step-by-step explanation:
Confidence Interval for Proportion =
p ± z ×√p(1 - p/n)
p = proportion = x /n
x = 71
n = 635
p = 71/635
p = 0.1118110236
p ≈ 0.1118
z score for 90% confidence interval = 1.645
Confidence Interval =
0.1118 ± 1.645 × √0.1118 (1 - 0.1118)/635
0.1118 ± 1.645 × √0.09930076/635
0.1118 ± 1.645 × √0.0001563791
0.1118 ± 1.645 × 0.0125051629
0.1118 ± 0.020570993
Confidence Interval =
0.1118 - 0.020570993
= 0.091229007
Approximately to the nearest hundredth ≈ 0.09
0.1118 + 0.020570993
= 0.132370993
Approximately to the nearest hundredth = 0.13
Therefore, the confidence interval for this proportion = (0.09, 0.13)
The 90% confidence interval for the given population proportion is (0.09,0.13) and this can be determined by using the formula of the confidence interval.
Given :
- Edwin defined the label "smoking regularly" for males smoking 30 or more cigarettes in a day and for females smoking 20 or more.
- Out of 635 persons who took part in the survey, 71 are labeled as people who smoke regularly.
The following steps can be used in order to determine the 90% confidence interval:
Step 1 - The formula of the confidence interval is used in order to determine the 90% confidence interval.
[tex]CI = p\pm z\sqrt{\dfrac{p(1-p)}{n}}[/tex]
Step 2 - Now, substitute the values of p, n, and z in the above expression.
[tex]CI = 0.1118\pm 1.645\sqrt{\dfrac{0.1118(1-0.1118)}{635}}[/tex]
Step 3 - Simplify the above expression.
[tex]CI = 0.1118\pm 1.645\times 0.0125051629[/tex]
[tex]CI = 0.1118\pm 0.020570993[/tex]
So, the 90% confidence interval for the given population proportion is (0.09,0.13).
For more information, refer to the link given below:
https://brainly.com/question/2396419
