A Do-It-Yourself Homeowner Is Installing a New Toilet

question 38

Essay

A do-it-yourself homeowner is installing a new toilet. While installing the toilet he must decide on what kind of connecting pipe he will install to the water supply. There are two available options, one that has a shut-off valve in case of a leak and a cheaper one without the shut-off valve. Suppose that the shut-off valve pipe costs an extra ten dollars and that the homeowner must buy one of the two.
(a) Draw a decision tree for this scenario, labeling the cost of a leak as X and the chance of a leak as P.
(b) If the chance of a leak causing household damage is 1%, at what $ amount of household damage is the owner neutral on which pipe to buy?
(c) If the cost of a leak would be $10,000 what is the maximum % chance to leak at which the homeowner would prefer to buy the cheaper pipe?
(d) If the cost of a leak is $1,000 and the chance to flood .1% which pipe should the homeowner buy?

---

Definitions:

P-value

The chance of getting test outcomes that are as drastic as or more than the observed results, given that the null hypothesis holds.

Song Ratings

An evaluative score or feedback provided to songs, often used for recommendations, trending analysis, or ranking systems.

Friedman Test

An analysis technique without reliance on parameter assumptions for discerning treatment disparities across multiple testing occasions.

Distribution

The way in which something is shared out among a group or spread over an area, or the set of all possible values of a variable and how frequently they occur.