Question

Express the confidence interval in the form of .

Answer 1

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 $\hat{p}$ 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.