Question

# Question 1 The travel agency Paradise Retreats has developed a model to predict the price per...

Question 1

The travel agency Paradise Retreats has developed a model to predict the price per night of holiday apartment rentals in the coast of Croatia:

?=550+11?1−5?2

?: price of the apartment per night (in kunas)

?1: area of the apartment (in square meters)

?2: distance to the beach (in km)

How much more expensive (in kunas) will be the rental of a 60 square-meter apartment on the beachfront compared with a 60 square-meter apartment 10 km from the beach?

How much will the price per night decrease when the area of the apartment decreases by 20 square meters?

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Question 2

The summary output of Paradise Retreats' model in Excel is in the tables below:

Regression Statistics
Multiple R 0.764437898
R Square 0.5843653
Standard Error 315.8931794
Observations 60
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 550 317.1379944 0.110883586 0.912472524 -613.4546286 683.785425
x1 11 7.187801286 1.304664049 0.202266328 -5.323038326 24.07837018
x2 5 9.990263453 3.509123492 0.001488311 14.62468522 55.48945112

A) This regression model explains less than 60% of the variation of the price per night.

B) The area of the apartment is not significant at a confidence level of 95%.

C) The area of the apartment is not significant at a confidence level of 99%.

D) The area of the apartment is significant at a confidence level of 99%.

E) The distance to the beach is not significant at a confidence level of 99%.

F) None of the above.

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Question 3

Paradise Retreats offer a wide range of options for an unforgettable holiday in Croatia. Their portfolio includes apartments on the coast and cabins in the mountains. On average, their customers book many more apartments than cabins every month. Paradise Retreats analyzed some historical data, did a chi-squared test and confirmed that the number of apartments booked every month follows a normal distribution with an average of 23 and a standard deviation of 7.

What is the probability that more than 29 apartments are booked through Paradise Retreats in a month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).

What is the probability that less than 21 apartments are booked through Paradise Retreats in a month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).

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Question 4

The number of mountain cabins that are booked through Paradise Retreats every month follows a Poisson distribution with a mean of 4. At Paradise Retreats, they are considering to reduce the number of cabins included in their portfolio.

What is the probability that at least one cabin is booked through Paradise Retreats in any given month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).

If Paradise Retreats only has 3 cabins available for rent, what is the probability of not meeting the demand for cabins during a given month?

Write your answer not as a percentage, but as a decimal number with 4 decimal places (e.g. if the probability is 87.56%, write 0.8756 in the answer box).