Question

A sleeping bag is tested to withstand temperatures of$-15°\mathrm{F}$. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.

Short answer

Type I error: Although the bag can tolerate temperatures as low as -$15°F$, you infer that it cannot.

Type II error: The bag isn't designed to survive temperatures below -$15°F$, but you assume it can.

Step-by-step solution

Given Information

A sleeping bag has been tested to endure temperatures as low as -${15}^{\circ }F$Assume the bag won't be able to withstand those temperatures.

Concept Used

When running a hypothesis test, there are four possible results depending on whether the null hypothesis $H_0$is true (or untrue) and whether or not to reject it.

1. When $H_0$is true, the decision is not to reject him.

2. When $H_0$is true, the decision is to reject $H_0$.

3. When $H_0$is false, the decision is not to dismiss him.

4. When $H_0$is false, the decision is to reject $H_0$.

Explanation

The following are the Type I and Type Il errors for the given hypothesis:

Type I error: Although the bag can tolerate temperatures as low as -$15°F$, you infer that it cannot.

Type II error: The bag isn't designed to survive temperatures below -$15°F$, but you assume it can.