Respuesta :
Answer:
[tex] (Lower=0.61, Upper=0.91) [/tex]
And using the property of symmetry for the confidence interval we can estimate the sample proportion [tex]\hat p[/tex] with this formula:
[tex]\hat p =\frac{Upper-Lower}{2}= \frac{0.91-0.61}{2}= 0.15[/tex]
The final answer for this case would be:
[tex]\hat p= 0.15[/tex]
So approximately 15% of teenagers have a sibling.
Step-by-step explanation:
For this case we assume that the proportion of interest is [tex]p[/tex] who represent the number of teenagers who have a sibling and in order to estimate this proportion we can conduct a confidence interval.
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And for this case the confidence interval is given by:
[tex] (Lower=0.61, Upper=0.91) [/tex]
And using the property of symmetry for the confidence interval we can estimate the sample proportion [tex]\hat p[/tex] with this formula:
[tex]\hat p =\frac{Upper-Lower}{2}= \frac{0.91-0.61}{2}= 0.15[/tex]
The final answer for this case would be:
[tex]\hat p= 0.15[/tex]
So approximately 15% of teenagers have a sibling.
Sample proportion p is 0.15 . It means that 15 % teenagers have a sibling.
Since, confidence interval for the proportion of teenagers who have a sibling is given that, (0.61,0.91)
Lower value = 0.61 , upper value = 0.91
Sample proportion is computed by formula shown below,
Sample proportion, [tex]p=\frac{upper-lower}{2}[/tex]
Thus, sample proportion, [tex]p=\frac{0.91-0.61}{2}=0.15[/tex]
Hence, Sample proportion p is 0.15 . It means that 15 % teenagers have a sibling.
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