Question

Question 2) Parking Costs and Proximity to City

Brett, an analyst working for a company that looks after a suite of parking stations, asserts that the cost of parking significantly increases for customers as the location of a restaurant at which they patron is located closer to the city.

Select a suitable graphical method and numerical measure to examine whether this to be the case using the data you have been provided.

Examining your graphical results, can you see whether, and why, there is a further consideration in the data that should be explored? In particular, repeat your analysis above by segmenting the data based on restaurants located in the City and Metro regions combined (i.e., those restaurants that are 10km or less in distance from the CBD) as compared to those located in the outer suburbs (i.e., at a location that is more than 10km from the CBD).

To be clear, you are asked to provide three figures and three numerical measures to answer this question in its entirety.

Write a short summary that describes these results to Brett and suggest possible reasons why the results vary depending on how the data is segmented. Is there an additional way of measuring the distance variable that you could propose that could be useful to explain the variation in parking costs not captured presently?

extra info:

DATA DICTIONARY

Variable

Description and coding notes

OBS

Observation (arbitary order)

RESTID

Identification of restaurant

RESTLOC

Location of restaurant (City is within 5km of CBD; Metro is 5-10km; Outer is more than 10km from CBD)

1

City - Harbour

2

City - Downtown

3

Metro - North

4

Metro - South

5

Metro - East

6

Metro - West

7

Outer - North

8

Outer - South

9

Outer - East

10

Outer - West

CITY123

1 = City; 2=Metro; 3=Outer as above.

KM2CITY

Kilometres restaurant is from city CBD.

COSTfor2

Average price of restaurant (for two people) in $AUD

Breakfast

Whether resturant is open for breakfast (1=yes; 0=No)

Lunch

Whether resturant is open for lunch (1=yes; 0=No)

Dinner

Whether resturant is open for dinner (1=yes; 0=No)

Cuisine

Type of cuisine served at restaurant / classification

1

Cofee/Café

2

Pizza/Pizzeria

3

Chinese

4

Italian

5

Modern Australian

6

Thai

7

Japanese

8

Indian

9

Greek

10

Korean

HLTHrate

Perceived rating of restaurant with respect to healthiness (based on consumer perceptions)

1 = Very unhealthy; 2=Unhealthy; 3=Healthy; 4=Very healthy

Outdoor

Whether restaurant has outdoor seating (1=Yes; 0=No)

WaterVw

Whether restaurant has water views (1=Yes; 0=No)

GlutFree

Whether restaurant has adeqaute gluten-free options (1=Yes; 0=No)

Whlchr

Whether restaurant is wheelchair accessible (1=Yes; 0=No)

Alchohol

Whether restaurant serves alcohol (1=Yes; 0=No)

KidFriendly

Whether restaurant appears to cater for children / families (1=Yes; 0=No)

PetFriend

Whether restaurant is pet friendly (1=Yes; 0=No)

ParkDist

Distance to parking station or similar (in metres)

CostPark2Hrs

Cost of parking at station or similar for a two hour period.

Prox2Cinema

How close restaurant is to cinema (in metres)

CustRating

Rating of customers (index is from 0 to 100 where 0 is worst rated restaurants and 100 is best rated restaurants; more than 50 is 'good')

Answer 1

Solution:

• By pulling out the data of rows L and V from the spreadsheet, the summary statistics are obtained as per below

  	Outdoor - Yes	Outdoor - No
  Population Size	424	888
  Mean	57.7004717	50.86599099
  Standard Deviation	16.56967564	16.32251847

  Hypothesis Test for Restaurants with Outdoor Seating

  

  

  

  This is a very high test statistic, i.e. we have a highly significant result in favour of the null hypothesis. The P-value is practically zero.

  

  We reject the null hypothesis and conclude that outdoor seating restaurants have a rating higher than 50.

  

  

  

  Hypothesis Test for Restaurants without Outdoor Seating

  

  

  

  

  Assuming the common alpha value of 0.05, then we fail to reject the null hypothesis. That is, we do not have a significant result. Hence, we conclude that outdoor seating restaurants do not have a rating higher than 50.

  

  

  

  Note that there is no overlap between the 95% confidence intervals for restaurants with, against those without outdoor seating. Hence, we conclude that the restaurants with outdoor seating do receive a higher rating than those that do not. This can be represented in a combined sketch of the two rating distributions, as below