Respuesta :
Answer:
[tex]0.625 \pm 1.645*0.0571[/tex]
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
[tex]\pi[/tex] is the estimate
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex], also called the critical value.
The standard error is:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level critical value
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.955[/tex], so [tex]z = 1.645[/tex].
Estimate:
72 petty theft cases and finds 45 of these have gone unsolved.
So [tex]\pi = \frac{45}{72} = 0.625[/tex]
Standard error:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.625*0.375}{72}} = 0.0571[/tex]
Answer:
[tex]0.625 \pm 1.645*0.0571[/tex]
