Question

The average hotel price in Moscow is $216 per night with a standard deviation of $32. The average hotel price in Cancun is $161 per night with a standard deviation of $22. The average hotel price in Bangkok is $100 per night with a standard deviation of $17. A room at the Emerald Hotel in Moscow costs $200 per night, a room at the Ocean View Hotel in Cancun costs $183 per night, and a room at the Emperor Hotel in Bangkok costs $120 per night.

Required:
Which hotel is more expensive compared to other hotels in its city?

Answer 1

The Emperor Hotel in Bangkok has the higher z-score, so it is more expensive compared to other hotels in its city.

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

The most expensive hotel has the higher z-score. So

Emerald Hotel in Moscow:

Costs $200, which means that
`X = 200`

The average hotel price in Moscow is $216 per night with a standard deviation of $32, which means that
`\mu = 216, \sigma = 32`. So

`Z = (X - \mu)/(\sigma)`

`Z = (200 - 216)/(32)`

`Z = -0.5`

Ocean View Hotel in Cancun

Costs $183, which means that
`X = 183`.

The average hotel price in Cancun is $161 per night with a standard deviation of $22, which means that
`\mu = 161, \sigma = 22`. So

`Z = (X - \mu)/(\sigma)`

`Z = (183 - 161)/(22)`

`Z = 1`

Emperor Hotel in Bangkok

Costs $120, which means that
`X = 120`.

The average hotel price in Bangkok is $100 per night with a standard deviation of $17, which means that
`\mu = 100, \sigma = 17`. So

`Z = (X - \mu)/(\sigma)`

`Z = (120 - 100)/(17)`

`Z = 1.18`

The Emperor Hotel in Bangkok has the higher z-score, so it is more expensive compared to other hotels in its city.