Answer:
a)0.519
b)requirements for constructing a confidence interval about p are satisfied.
c)0.488, and 0.550
d)yes this is because there is no possibility
that the true proportion is not captured in the confidence interval.
e)
0.450, 0.512
Explanation:
a)The point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without can be calculated as
521 of that adult that indicated that televisions are a luxury they could do without/1003 adults surveyed,
p = 521/1003
= 0.519.
b)
np(1-p)=1003×(0.519)×(1-0.519)
=250.39≥10 and the sample size is less than 5% of the population
therefore, requirements for constructing a confidence interval about p are satisfied.
c) we were given 95% confidence,
Then α=(1-0.95)
= 0.05
From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96
confidence interval can the be calculated using the formula below
- p ± Z*√ p (1 – p)/n
=0.519 ± 1.96√0.519×(1 – 0.519)/(1003)
= 0.519 ± 1.96×0.0158
0.519 ± 0.031
= 0.488, and 0.550
d) yes this is because there is no possibility
that the true proportion is not captured in the confidence interval.
e)the sample size can be calculated as
P=x/n
=(1003-521)/1003
=0.481
But we're given 95% confidence interval
Then
α=(1-0.95)=
0.05
From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96
Then convidence interval=
- p ± Z*√ p (1 – p)/n
=0.481 ± 1.96√0.481×(1 – 0.481)/(1003)
0.450, 0.512