# Statistics – Confidence Interval / Null Hypothesis

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Name: ____________________
11

5

.

10

ID Number: ( ( ( ( ( ( ( (

Assignment

3

Due

2

4

th January

20

13

Q1
The owner of a petrol station wants to study fuel-purchasing habits of motorists at his station. A random sample of

60

motorists during a particular week gave the following results:

Amount purchased:

x

=

42

.8 litres, S =11.

7

litres.

9 motorists purchased diesel.

(a)
Set up a 95% confidence interval estimate for the proportion of motorists who buy diesel. Write a sentence to explain the meaning of your answer.

[2]

(b)
Test at the 5% level whether there is evidence that the mean amount purchased is more than 40 litres.

[5]

(c)
Before carrying out the survey, the owner thought that 10% of his customers used diesel. Do the results of the survey suggest that he was wrong? Explain.

[2]

(d)
Do we need to assume for the analysis in (b) that the amounts purchased follow a normal distribution? Discuss.

[2]

Q2
The data file PHONE2.xls gives the time (in minutes) to answer a sample of 40 queries made to a call centre. Two different call centre teams are employed, and 20 calls were sampled from each team.

(a)
Is there evidence (at 5% level) of a difference in mean answering time between the two call centre teams?

[5]

(b)
Produce a side-by-side box-and-whisker plot for the answering times. What does this suggest about the differences between Team 1 and Team 2?

[3]

Q3
The data file FRUITVEG.xls compares prices for a range of items at a fruit and vegetable shop and a nearby supermarket.

(a)
Test at the .05 level of significance whether on average prices are higher at the fruit shop than at the supermarket.

[4]

(b)
Explain why a paired test is more appropriate here than a test for independent samples.

[2]

Q4
A sales manager for a computer firm has estimated that older employees of potential customers of bulk purchase orders personally use less powerful and less complex systems than younger employees, and are less likely to be receptive to new sales promotions emphasizing more power and complexity in the machines. Data collected for 238 executives, divided into young, middle and older age groups, show the level of power and complexity in their personally owned machines.

Age

Computer Power

Young

Middle

Older

Total

(Simple) Level 1

10

12

20 42 2

18

12

17

47

3

19

18

21

58

4

22

31

7 60 5

24

5

2

31

(a)
Use a chi-squared test to determine whether there is any relationship between the age of the executive and the power and complexity of their personal computer.

[5]

(b)
By comparing the observed and expected frequencies, explain briefly the main difference in power and complexity of their personal computer between younger and older travelers. How might this be useful to the sales manager?

[2]

+ + + + + +

Null hypothesis:

Alternative hypothesis:

p-value:

Decision:

Null hypothesis:
Alternative hypothesis:
p-value:

Decision:

[2]

Null hypothesis:

Alternative hypothesis:
p-value:
Decision:

Null hypothesis:

Alternative hypothesis:

Expected frequencies:

Age�

Power�

Young�

Middle�

Old�

Total�

1�

4

2�

2�

47�

3�

58�

4�

60�

5�

31�

Total�

93�

78�

67�

238�

p-value:

Conclusion:

115.101/Ass3/1203
2

_1404281299.unknown

## Data

2.49 3.98

1.49

2.49

 Fruit and Vegetable Prices Fruit Shop Supermarket Bananas (kg) 1.49 2.45 Broccoli (kg) 2.49 3.98 Mushrooms (kg) 4.99 7.98 Nectarines (kg) 3.99 5.48 Strawberries (250g) Green Grapes (kg) 9.99 4.97 Hydroponic Lettuce 0.88 Potatoes (kg) 2.98 Carrots (kg) 1.99 1.98 Snow Peas (kg) 11.99 9.98

2

>ForBoxWhiskerPlot

2

0.6 1 1

0.6

1

0.5 1 2

1.52 1 1 2.5
1.52 1.5 1 3

0.5 1.5 2

2.29 1 1.5 2.5
2.29 1.5 1.5 3

0.5 2 2

3.93 1 2 2.5
3.93 1.5 2 3

0.5 2 2

7.55 1 2 2.5
7.55 1.5 2 3

0.6 1 1 2.5
7.55 1 2 2.5
1.52 0.5 1 2
3.93 0.5 2 2
1.52 1.5 1 3
3.93 1.5 2 3

 0.6 0.5 1 2.5 1.5 3 1.52 2.29 3.93 7.55

## ForBoxWhiskerPlot2

0.5

0.6 2
0.8 1 0.6 2.5
0.8 1.5 0.6 3
1.52 0.5

1.52 2
1.52 1 1.52 2.5
1.52 1.5 1.52 3

0.5

2

2.63 1 2.1 2.5
2.63 1.5 2.1 3

0.5

2

3.97 1 3.75 2.5
3.97 1.5 3.75 3

0.5

7.55 2
6.32 1 7.55 2.5
6.32 1.5 7.55 3

0.8 1 0.6 2.5
6.32 1 7.55 2.5
1.52 0.5 1.52 2
3.97 0.5 3.75 2
1.52 1.5 1.52 3
3.97 1.5 3.75 3

 0.8 2.63 2.1 3.97 3.75 6.32

## Data

1

1

1

1

1.52 1

1

1

3.97 1

1

1

1

1

1

1.6 1

0.8 1

1

6.32 1
3.93 1

1

1

7.55 2
3.75 2
2.1 2

2

0.6 2
1.52 2

2

2.1 2

2

2

3.75 2

2

2

1.6 2

2

2

2

2

2

2

 Time Team 1.58 1.75 2.78 2.85 1.6 4.15 2.48 3.1 1.02 3.53 0.93 4.05 5.45 0.97 1.1 3.3 2.58 4.02 0.65 1.92 1.53 4.23 3.08 1.48 1.65 4.72