Green & Fast Motor (GFM) manufactures passenger cars. It equips its cars with Power tyres

supplied by the Power Drive Corporation (PDC), before delivering them to its two regional

distributors located in the East and West of the country. PDC's product information shows that

the lifespan of a Power tyre follows a Normal Distribution with mean value of 40000 kilometres

(km) and standard deviation of 2000 km.

(a) GFM's management wants to understand more about the Power tyres.

(i) Find the distance that 80% of the Power tyres can last beyond.

(ii) The company's Data Analyst wants to take a sample of Power tyres to study their

performances. He took data from only 12 tyres as he is constrained by time and

resources for the analysis. Evaluate the probability that the mean lifespan of these

12 tyres will be at least 41000 km. Explain why the Analyst can use a small sample

size.

(b) Eco Earth Enterprise (EEE) has developed its new Eco tyre based on the latest synthetic

material. While promoting its tyre to SFM, EEE's Sales Director boasted that Eco tyre

provides better fuel efficiency (measured in km/litre) than Power tyre for vehicles.

GFM's management bought one shipment of Eco tyres. It equipped the cars for its East

Region distributor with Eco tyres while those for the West Region distributor continued

to use Power tyres. A sample of cars sold by each distribution is monitored and the cars'

fuel efficiencies are recorded as shown in the data file

(Fuel_Efficiencies_Eco_n_Power.xlsx).

FE with Power tyres	FE with Eco tyres
10.30	11.30
11.10	10.90
11.50	11.40
7.70	11.90
12.90	11.30
10.70	11.90
9.90	8.00
11.70	12.10
9.70	11.10
10.00	11.20
10.00	9.00
9.10	12.00
10.60	8.80
8.90	13.20
9.80	9.40
12.00	11.00
11.10	9.70
11.00	10.90
12.70	12.40
9.30	12.70
10.10	11.60
10.10	11.70
9.20	9.30
10.70	8.50
10.10
10.10

Use Microsoft Excel to summarise separately the two (2) samples of data on the cars'

fuel efficiencies. Identify the locations and spreads of the samples, each with a measure

that takes all data into consideration. Comment on their differences.

Present the data in an appropriate type of diagram. Comment on the data distributions.

(c) Using the Excel summary output in Q1(b), identify the 95% Confidence Interval (CI)

estimate of the mean fuel efficiency for each type of tyre used and interpret this

confidence interval. Hence infer any differences in the fuel efficiencies provided by the

two (2) different tyres.

State the requirement in using t-distributions to construct the confidence intervals.

Justify whether this requirement is met in both cases.