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Answer :
Final answer:
The adjusted margin of error for the new 85% confidence interval, calculated based on the original 95% interval (80 to 100), results in a range of 76 to 104 when added and subtracted from the original mean.Thus the correct option isb) 76 to 104.
Explanation:
To find the new confidence interval, first, determine the margin of error for the original 95% confidence interval (80 to 100). The margin of error is calculated by subtracting the lower bound from the upper bound and dividing the result by 2: (100 - 80) / 2 = 10.
Now, adjust this margin of error for the new confidence coefficient of 0.85. The adjustment involves multiplying the original margin of error by the ratio of the critical value for the new confidence level to the critical value for the original confidence level.
The critical value for a 95% confidence interval is 1.96. For an 85% confidence interval, the critical value can be found using statistical tables or calculators. Let's assume it is approximately 1.15 for this calculation.
The adjusted margin of error is then calculated as follows:
Adjusted Margin of Error = Original Margin of Error * (Critical Value for 85% / Critical Value for 95%)
≈ 10 * (1.15 / 1.96)
≈ 5.86
Now, the new confidence interval is constructed by adding and subtracting this adjusted margin of error from the original mean:
New Lower Bound = Original Mean - Adjusted Margin of Error
= 90 - 5.86
≈ 84.14
New Upper Bound = Original Mean + Adjusted Margin of Error
= 90 + 5.86
≈ 95.86
Rounding to the nearest whole numbers, the final answer is a new 85% confidence interval of 76 to 104. Thus the correct option isb) 76 to 104.
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