Question 1

A sports shop selects a random sample and records the sales of items made in China and those

made in America.

Country of Origin n Mean Std. Deviation

China 50 22.5 9.75

America 33 33.15 11.6

a) What is the SE Mean for the sales from China? [2]

b) Calculate a 95% confidence interval for the mean sales amount made in America [4]

Question 2

The probability that a rose bud blooms is p. In a random sample of 500 rose buds, 240 of them

bloomed.

With the data obtained in a random sample, a hypothesis test at the 1% level of significance is

carried out to determine whether p is different from 0.45.

a) State the null and alternative hypothesis [2]

b) Calculate the test Statistics [2]

c) What is the p-value of the test? [2]

d) Supporting your answer, state the conclusion of the test [3]

Question 3

Workers at a private business was given a grade (A, B, C) based on their yearly performance. The

data was recorded along with the department they belong. The results obtained using MINITAB are

shown below:

Expected counts are printed below observed counts

A B C Total

Accounting

12 8 7

(12.960) (7.830) (6.210) *

Sales

17 10 8

(16.800) (10.150) (8.050) 35

Marketing

19 11 8

(18.240) (**) (8.740) 38

Total 48 29 23 100

Chi-sq = 0.0711 + 0.0037 + 0.1005 +

0.0024 + 0.0022 + 0.0003 +

0.0317 + 0.0000 + *** =0.2746

DF = ??, p-value = ???

a) Carefully define the null and alternative hypotheses of the 2 test of the above table. [2]

b) Find the missing values '*', '**', '***' ??, ??? [8]

c) What is the conclusion of this test? Give reasons for your answer. [3]

Question 4

Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the

company wants to know how different variables affect the sales of his vehicles. A random sample of

yearly data was taken with the view to testing the model:

SALES=+AGE+MIL+ENG

Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIL= the total

mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was

processed using MINITAB and the following is an extract of the output obtained:

The regression equation is *****

Predictor

Coef StDev t-ratio p-value

Constant 1.7586 0.2525 6.9648 0.0000

AGE 0.2124 0.3175 * 0.5042

MIL -0.7527 0.3586 -2.0991 **

ENG 4.8124 0.6196 7.7664 0.0000

R-sq=56.1% R-sq(adj) =59.8%

Analysis of Variance

Source DF SS MS F p

Regression 3 413.1291 138.7097 *** 0.00

Error 50 457.7607 2.2888

Total 53

a) What is dependent and independent variables? [2]

b) Fully write out the regression equation [1]

c) Fill in the missing values '*', '**', '***'and '***'. [4]

d) Hence test whether is significant. Give reasons for your answer. [4]

e) Perform the F Test making sure to state the null and alternative hypothesis. [4]

f) Given an interpretation of the term "R-sq" and comment on its value. [2]