A hotel installs smoke detectors with adjustable sensitivity in all public guest rooms. (a) State the null and alternative hypotheses. There is no fire There is a fire (b) Define Type I and II errors. A smoke detector sounds an alarm when there is no fire A smoke detector does not sound an alarm when there is a fire (c) In this case, which type of error has the more severe consequences

(a) H₀: There is no fire vs. Hₐ: There is a fire.

(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

(c) In this case, type II error has the more severe consequences.

Step-by-step explanation:

It is provided that a hotel installs smoke detectors with adjustable sensitivity in all public guest rooms.

(a)

The hypothesis can be defined as follows:

H₀: There is no fire.

Hₐ: There is a fire.

(b)

A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

In this case a type I error will be committed if we conclude that there is a fire and the smoke detector sounds an alarm, when in fact there is no fire.

In this case a type II error will be committed if we conclude that there is no fire and the smoke detector does not sounds an alarm, when in fact there is a fire.

(c)

In this case, type II error has the more severe consequences.

Concluding that there is no fire as the smoke detector did not sound an alarm, when in fact there is a fire, will cause casualties and is harmful for the health of the guests.

Guests would not be alert about the fire as there was not any alarm, and many may loose their lives because of this.