• Calculate a confidence interval and explain what it means.
• Recognize common misinterpretations of confidence intervals.

Wear Sunscreen!

According to the Centers for Disease Control and Prevention (CDC), when you are outdoors, you may be exposed to the sun’s harmful ultraviolet (UV) rays. You are at the highest risk for UV exposure when you are traveling near the equator, during summer months, at high elevations, or between [latex]10[/latex]AM to [latex]4[/latex]PM. You can also be exposed to UV rays on cloudy days and during the winter. UV rays reflect on the snow, sand, and water.

Without protection from the sun’s ultraviolet (UV) rays, damage can be done to your skin in as little as [latex]15[/latex] minutes. Over time, this damage can increase the risk of developing skin cancer; thus, it is important to always practice “sun safety,” such as wearing sunscreen and sunglasses and taking breaks in the shade.^[1]

Conditions for confidence intervals for proportions 

When constructing confidence intervals for a proportion, remember that it is important to first confirm that the following conditions are met:

• Random sampling is used.
• The sample is less than [latex]10\%[/latex] of the population. (Although it is not specified, we can typically assume that the sample is less than [latex]10\%[/latex] of the population.)
• The sample is large enough that [latex]n\hat{p} \geq 10[/latex] and [latex]n(1 − \hat{p}) \geq 10[/latex].

[Trouble viewing? Click to open in a new tab.]

---