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Answer:
The 90% confidence interval for p is (0.8236, 0.9564). The upper confidence limit for p is 0.9564.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
He discovers that a particular weed killer is effective 89% of the time. Suppose that this estimate was based on a random sample of 60 applications.
This means that [tex]\pi = 0.89, n = 60[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 - 1.645\sqrt{\frac{0.89*0.11}{60}} = 0.8236[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 + 1.645\sqrt{\frac{0.89*0.11}{60}} = 0.9564[/tex]
The 90% confidence interval for p is (0.8236, 0.9564). The upper confidence limit for p is 0.9564.
Answer:
Answer:
The 90% confidence interval for p is (0.8236, 0.9564). The upper confidence limit for p is 0.9564.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
He discovers that a particular weed killer is effective 89% of the time. Suppose that this estimate was based on a random sample of 60 applications.
This means that
90% confidence level
So , z is the value of Z that has a pvalue of , so .
The lower limit of this interval is:
The upper limit of this interval is:
The 90% confidence interval for p is (0.8236, 0.9564). The upper confidence limit for p is 0.9564
Step-by-step explanation:
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