Question

19. Housing in San Jose How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units in San Jose,
California:

Let X = the number of rooms in a randomly selected owner-occupied unit and Y = the number of rooms in a randomly chosen renter-occupied unit.
(a) Make histograms suitable for comparing the probability distributions of X and Y. Describe any differences that you observe.
(b) Find the mean number of rooms for both types of housing unit. Explain why this difference makes sense.
(c) Find the standard deviations of both X and Y. Explain why this difference makes sense.

Short answer

(a) Owners have better rooms than renters. Distribution for owners is roughly symmetric, while the allocation for renters is right-skewed.

(b) The mean for house owned is $6.280$and for house rented is $4.187$.

(c) The standard deviation of both $X$and $Y$are $1.63$ and $1.31$.

Step-by-step solution

Part (a) Step 1: Given information 

Given in the question is a table , we have to consider $X=$the number of rooms in a randomly selected owner-occupied unit and $Y=$the number of rooms in a randomly chosen renter-occupied unit.

We need to make histograms suitable for comparing the probability distributions of $X$and $Y$.

Part (a) Step 2: Graphical Representation 

Housing in San Joise had the following histograms:

Part (a) Step 3: Graphical Representation

The histogram for rented housing in San Joise is as follows:

According to the graph, the owners have more rooms than the tenants. Owned has a generally symmetric distribution, while rented has a roughly right-skewed distribution.

The owned center has about six rooms, whereas the rented facility has about four rooms. Both histograms have nearly the same spread.

Part (b) Step 1: Given information 

Given in the question that, the distributions of the number of rooms for owner-occupied units and renter-occupied units in San Jose.

We have to find the mean number of rooms for both types of housing unit.

Part (b) Step 2: Explanation 

Let's compute the mean for house owned by using the Ti-83 calculator as follow:

Compute the mean for a rental residence using the Ti-83 calculator as follows:

Because of the different types of distributions, there is a discrepancy in the two means.

Part (c) Step 1: Given information 

Given in the question that, the distributions of the number of rooms for owner-occupied units and renter-occupied units in San Jose,

We have to compute the value for the standard deviations of both $X$and $Y$.

Part (c) Step 2: Explanation 

To compute standard deviation, use the calculator Ti-83 as follows: