Answer:
0.075 - 0.022 < p < 0.075 + 0.022
Do not evaluate each of the math expressions above.
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Explanation:
The given confidence interval is in the form (L, U)
- L = lower bound = 0.053
- U = upper bound = 0.097
Find the midpoint of L and U to get
(L+U)/2 = (0.053+0.097)/2 = 0.075
This is the value of [tex]\hat{p}[/tex] which is the symbol p-hat or phat (both pronounced the same). It's the sample proportion.
To get the margin of error E, we could do either of the following
- E = (U-L)/2 = (0.097-0.053)/2 = 0.022
- E = U - phat = 0.097 - 0.075 = 0.022
- E = phat - L = 0.075 - 0.053 = 0.022
This value of E represents half the width of the confidence interval. The full width being U-L.
