Answer:
a
i. Proportion
b
Best point estimate is [tex]\^ p = 0.60[/tex]
c
[tex]z_{\frac{\alpha }{2} } = 2.58 [/tex]
d
[tex]E = 0.0206 [/tex]
e
[tex] 0.5794 < p < 0.6206 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 3765
The proportion that feel the businesses in Laradise, are run by compliant individuals is [tex]\^ p = 0.60[/tex]
Considering question a
The correct option is Proportion because in the prompt we are told to obtain the fraction of the total sample size that has a particular attribute (which their opinion of business in Laradise) and this is what a proportion represents
Considering question b
The best point estimate is [tex]\^ p = 0.60[/tex] because this proportion best defines the fraction of the sample size who feel the businesses in Laradise, are run by compliant individuals
Considering question c
Generally given that the sample size is large enough n > 30 , it then means that the distribution is approximately normal so
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]z_{\frac{\alpha }{2} } = 2.58 [/tex]
Considering question d
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 2.58 * \sqrt{\frac{ 0.60 (1- 0.60 )}{ 3765} } [/tex]
=> [tex]E = 0.0206 [/tex]
Considering question e
Generally 99% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex] 0.60 -0.0206 < p < 0.60 + 0.0206[/tex]
=> [tex] 0.5794 < p < 0.6206 [/tex]
