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Sagot :
Answer:
See below
Step-by-step explanation:
Check One Sample Z-Interval Conditions
Simple Random Sample? √
np≥10? √
n(1-p)≥10? √
One-Sample Z-Interval Information
- Formula --> [tex]CI=\hat{p}\pm z^*\biggr(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\biggr)[/tex]
- Sample Proportion --> [tex]\hat{p}=\frac{54}{250}=0.216[/tex]
- Critical Value --> [tex]z^*=1.4395[/tex] (for a 85% confidence level)
- Sample Size --> [tex]n=250[/tex]
- Margin of Error (MOE) --> [tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Problem 1
As stated previously, Anas should use the critical value [tex]z^*=1.4395[/tex] to construct the 85% confidence interval
Problem 2
Given our formula for the margin of error (MOE), the value is [tex]MOE=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\sqrt{\frac{0.216(1-0.216)}{250}}\approx0.026[/tex]
Problem 3
The 85% confidence interval would be [tex]CI=\hat{p}\pm z^*\biggr(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\biggr)=CI=0.216\pm 1.4395(0.026)\appro=\{0.1786,0.2534\}[/tex], which means that we are 85% confident that the true proportion of people that clicked on the advertisement is between 0.1786 (~45 people) and 0.2534 (~63 people)
Problem 4
Increasing the sample size to [tex]n=500[/tex] is going to decrease the margin of error because it is a closer representation of the population, but, alas, requires more time, energy, and resources to observe.
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