Respuesta :
Answer:
(B) The summer interval is wider and has a greater point estimate.
Step-by-step explanation:
Winter interval is (0.087, 0.133)
Confidence interval is given by
Lower limit = 0.087 = p-moe
Upper limit = 0.133 = p+moe
Where moe = margin of error
After adding both the equations
(0.087+0.133) = (p+p) + (moe-moe)
2p = 0.22
p = 0.11
After substituting the value of p in equation 0.087 = p-moe
Moe = 0.023
Therefore we know that moe = z*√{p*(1-p)/n}
Where z is the critical value of 95% confidence interval which is 1.96
P = 0.11
After substituting all the values
N = (1.96/0.023)^2 * 0.11*(1-0.11)
N = 710.950170132 = 711
In summer, p = 0.4 and n = 711(as it is mentioned that sample size is same)
Here moe = 1.96*√{0.4*(1-0.4)/711}
= 0.03601031263
CI
(P-moe, p+moe)
(0.364 to 0.436)
So by above calculation it is clear that summer interval has greater point estimate that is 0.4>0.11
Width of winter interval = 0.133-0.087 = 0.046
Width of summer interval = 0.436-0.364 = 0.072
Therefore it is obvious that summer interval is wider
Therefore the correct answer is ,summer interval is wider and has greater point estimate.
