Express the confidence interval (0.033,0.099) in the form of P-E<p<P+E
Assuming a normal distribution,
.066 - .033 < .066 < .066 +.033
To express the confidence interval (0.033, 0.099) in the form of P - E < p < P + E, we first need to find the middle point (P) of the interval and the margin of error (E).
1. Middle Point (P):
To find P, calculate the average of the two endpoints:
P = (0.033 + 0.099) / 2
P = 0.066
2. Margin of Error (E):
To find E, subtract the lower endpoint from the middle point:
E = P - lower endpoint
E = 0.066 - 0.033
E = 0.033
Now we can express the confidence interval (0.033, 0.099) as:
P - E < p < P + E
0.066 - 0.033 < p < 0.066 + 0.033
0.033 < p < 0.099
Therefore, the confidence interval (0.033, 0.099) can be expressed as 0.033 < p < 0.099
To express the given confidence interval (0.033, 0.099) in the form of P-E < p < P+E, we can calculate the midpoint and the margin of error.
1. Midpoint:
The midpoint is calculated by finding the average of the upper and lower bounds of the confidence interval:
Midpoint = (lower bound + upper bound) / 2
= (0.033 + 0.099) / 2
= 0.066
2. Margin of Error:
The margin of error is the half-width of the confidence interval, calculated by subtracting the lower bound from the midpoint (or vice versa):
Margin of Error = (Midpoint - Lower bound) = (Upper bound - Midpoint)
= (0.066 - 0.033) = (0.099 - 0.066)
= 0.033
Therefore, the confidence interval (0.033, 0.099) can be expressed as:
0.066 - 0.033 < p < 0.066 + 0.033