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MCD2080 – FAT 1

General Instructions
• The test is ‘closed book’ and must be completed during your lecture lesson 2 session.
• You have 45 minutes reading and writing time and 15 minutes uploading your answers on Moodle.
• This test is worth 5% of the trimester’s assessment.
• Only approved HP 10bII+ Financial Calculator and Excel are permitted.
• There are 2 questions.
• Write answers in the spaces provided in this booklet or plain paper and upload answers on Moodle
link provided.
• Answer all questions.

Hints
• If a question asks you to explain your answer, most (if not all) of the marks will be awarded for
the explanation of how the answer was obtained.
• Marks are awarded according to the quality of your answers, not for the amount written.



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Office Use Only
Question 1 2 TOTAL
Out of 7 13 20
Mark


MCD2080 FAT 1 Sample Solution guide 2

Question 1 [2.5 + 2.5 + 2 = 7 Marks]
a) A company claims the speed of octa-core processor of their new smart phone has a mean of
8 gigahertz (GHz) with a standard deviation of 0.75 GHz. Assuming that the population is
approximately normally distributed and using 68 – 95 – 99.7 rule (empirical rule), answer the
following questions
(i) About what percent of processors should get more than 9.5GHz?
9.5 GHz is 2 () above the (̅) of 8 GHz is the upper limit of 95% of the
processor speed
Therefore, the
(̅ > . ) = − (̅ < . )
= % − % − . %
= . %
You can sketch to illustrate.
(ii) If 0.15% of the processors had a speed less than x, find the value of x l.
̅ ± has 99.7% of the data. This means there is 0.3% is the upper and lower tail of
the data.
So 0.15% of the speed less than a value of x implies
̅ − = − ( × . ) = .



b) What is the probability of mean speed less than 7.75 GHz of the new smart phone processor
from a sample of 36? Show all working. A diagram may also be helpful.
is the mean processor speed of a smart phone (GHz)
~ (,
.

)
( < . ) = (
−

√
⁄
<
.−
.
√
⁄
)
= ( < . ) = .
(found using =NORM.DIST(7.75,8,(0.75/SQRT(36)),1) OR =NORM.S.DIST(2.00,1)

MCD2080 FAT 1 Sample Solution guide 3


Question 2 [1 + 1 + 1.5 + 1 + 4.5 + 2 + 2 = 13 Marks]
A supermarket manager is interested in customer transactions to assist with budgeting as well as
product placement throughout the store. Of particular interest to the manager is how long the
customer spends in the store and whether the customer uses a self-service register for their
transaction. Data has been collected from 400 customers and is provided in the file FAT 1 Version A
data.xlsx.
a) (i) Use Excel to produce a linear regression
SUMMARY
OUTPUT

Regression Statistics
Multiple R 0.764853
R Square 0.585
Adjusted R Square 0.582494
Standard Error 0.493339
Observations 400

ANOVA
df SS MS F Significance F
Regression 1 136.89 136.89 562.4458 3.8176E-78
Residual 399 97.11 0.243383
Total 400 234

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0 #N/A #N/A #N/A #N/A #N/A
Proportion 0.585 0.024666955 23.71594 3.29E-78 0.536506561 0.633493439

(ii) Use the regression output you produced in in part (i) state the 95% confidence interval for
the proportion of all customers who are female.
Lower limit = 0.537 Upper limit = 0.633
b) Interpret the confidence interval stated in part a)
We are 95% confident that the proportion of all customers (true/population proportion) who are
female lies between 53.7% and 63.3%.
c) The retail manager is also interested to know if there is a difference in average amount spent
for customers who are female and those who are male.

(i) Provide the Excel linear regression output for amount spent on gender.

MCD2080 FAT 1 Sample Solution guide 4

SUMMARY
OUTPUT

Regression Statistics
Multiple R 0.047051
R Square 0.002214
Adjusted R Square -0.00029
Standard Error 97.38731
Observations 400

ANOVA
df SS MS F Significance F
Regression 1 8375.236984 8375.237 0.883064 0.347933697
Residual 398 3774746.635 9484.288
Total 399 3783121.872

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 148.3852 7.558721137 19.631 1.7E-60 133.5252312 163.2452508
Gender 9.28681 9.882581173 0.939715 0.347934 -10.14177428 28.71539492
(ii) Use the regression you produced in part (i) to conduct a hypothesis test at the 5% level of
significance to determine if the amount spent is the same for customers who are female and
customers who are male.

1. Hypotheses: 2. Significance level:
: = OR : = = .
: ≠ : ≠
3. Test statistic and Critical value: 3. P-value:
Test statistic = 0.9397 P-value = 0.3479
Critical value = ⁄ ,−−
= . ⁄ ,−− = . OR
4. Decision and Conclusion:
Reject if t stat > t crit or t stat < -t crit Reject if p-value <
Since -1.9659 < 0.9397 < 1.9659 Since 0.3479 > 0.05
We cannot reject We cannot reject
We conclude that mean amount spent is the same for female customers and male customers
MCD2080 FAT 1 Sample Solution guide 5

a) What is a Type I Error in the context of this hypothesis test?
A Type I Error is rejecting when is true.
In the context of this hypothesis test that would be concluding that the mean amount spent by the
customers is different for female and females when actually if is the same.
b) What is a Type II Error in the context of this hypothesis test?
A Type II Error is not rejecting when is false.
In the context of this hypothesis test that would be concluding that the amount spent by the
customers is the same for female and females when actually if is the different