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The clinical literature reports that the duration of a typical cold is roughly 18 days. Researchers wanted to know if people tend to underestimate the duration of a typical cold, on average. They surveyed a random sample of 352 healthy adults in Georgia and asked them how long they think that a typical cold lasts. The researchers reported a 95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold.

Find the numerical value of the margin of error for the confidence interval.

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Answer:

0.65

Step-by-step explanation:

Confidence interval can be calculated using the Mean and Margin of error with M±ME where

  • M is the average expected cold days of typical cold.
  • ME is the Margin of error for the confidence interval.

In the question it is given that the researchers reported a 95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold.

The minimum value in the confidence interval is M-ME =6.9

The maximum value in the confidence interval is M+ME=8.2

Then we get 8.2-6.9=1.3=M+ME-(M-ME)=2× ME

From this we get ME=0.65

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