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Side$-$by$-$Side

Your company produces a sunblock lotion designed to protect the skin from both UVA and UVB exposure from the sun. You hire a company to compare your product with the product sold by your major competitor. The testing company exposes skin on the backs of a sample of $20$ people to UVA and UVB rays and measures the protection provided by each product. For $13$ of the subjects, your product provided better protection, while for the other $7$ subjects, your competitor's product provided better protection. Perform the two$-$sided significance test and report the results.

A two$-$sided significance test comparing the two products was previoiusly performed where success was defined as the outcome where your product provided better protection. Now, take the viewpoint of your competitor where success is defined to be the outcome where your competitor's product provides better protection. In other words, $n$ remains the same, but $x$ is now $7.$

Construct the $90\%$ confidence interval for this setting as an interval of percents. Assume the number of subjects is $75.$

Provide your answer as an interval in the form $($lower limit$,$ upper limit$).$ Give the limits to one decimal place.

$90\%$ confidence interval: