JV 804 Santa Monica College Maths and Stats for Business Questions I attached everything…………………………………………………. Module C

JV 804 Santa Monica College Maths and Stats for Business Questions I attached everything…………………………………………………. Module Code
JV804
Module Title
Maths & Stats for Business
Percentage of Final Grade
50%
Exam Code
JV804
Submission Date
Monday 20th April (1pm)
Submission Method
Email: maria.dunlop@stir.ac.uk
This assignment, which contributes 50%
towards your overall assessment on this
module, should be submitted as indicated
above. Failure to submit by the date/time
indicated will normally result in a zero
mark being assigned.
Your submitted assignment should
represent your own work. If I detect any
obvious instances of copying, I shall
normally assign a zero mark to each
assignment involved and the matter could
be taken further.
Instructions to Candidates:
1. Attempt all questions.
2. Show all your workings.
3. Formula sheet on last page of this question sheet.
4. Statistical tables on canvas.
Question 1 (40 marks)
The local council has recorded the number of books borrowed at a local library and the estimated
time spent reading per week as follows:
Id
Gender
Occupation
Time spent reading per
week (hours)
Number of books borrowed
per week
1
Male
Retired
5
2
2
Male
Retired
7
3
3
Male
Retired
4
2
4
Male
Retired
3
1
5
Female
Professor
10
5
6
Female
Retired
11
6
7
Male
Bus driver
8
4
8
Male
Retired
2
1
9
Male
Shop assistant
1
1
10
Female
Retired
15
7
11
Female
Retired
16
8
12
Female
Retired
14
7
13
Female
Teacher
19
10
14
Male
Taxi driver
2
1
15
Female
Retired
19
20
16
Male
Retired
7
2
17
Male
Cook
6
2
18
Female
Retired
14
7
19
Male
Nurse
5
2
20
Male
Policeman
6
3
21
Male
Gardener
4
2
22
Male
Sportsman
0
0
23
Male
Musician
1
1
24
Male
Teacher
2
2
25
Female
Retired
30
15
26
Male
Doctor
1
1
27
Female
Retired
20
10
28
Female
Retired
15
10
29
Male
Retired
1
1
30
Male
Retired
2
1
a) Analyse the occupations of the sample using a bar chart. Show all your work. (5 marks)
b) Construct a histogram analysing the reading time of female library users, clearly showing
all your work and choices. (5 marks)
c) Assuming the standard deviation is 3, construct a 98% confidence interval for the mean
number of books borrowed by the female users of the library. (10 marks)
d) The library staff assume that the average number of books borrowed per week by females
is 9 and the standard deviation is 3. Use a 5% significance level hypothesis test to show
whether the library should review their assumptions. (10 marks)
e) Construct a box plot analysing number of books borrowed by female customers (10 marks)
Question 2 (10 marks)
Students at a university studying Economics were tested on two papers (standard and advanced
level). The marks of 5 students are shown in the table below:Student
Number
Standard
Level Paper
Advanced
Level Paper
1
2
3
4
5
90
79
91
82
78
75
66
77
60
64
Calculate:
(i) The product moment correlation coefficient. (5 marks)
(ii) Spearman’s rank correlation coefficient. (5 marks)
Question 3 (7 marks)
A garden centre is interested in whether there is a relationship between their sales (£000s) and the
outdoor temperature. The table below shows results from a study carried out :Sales
Outdoor Temperature
Given the following values:
15
19
7
9
18
21
11
15
3
1
19
18
Sxy = 226.17 and Sxx = 284.83
Calculate the values of ‘a’ and ‘b’ for the regression model y = a + bx and write the
regression equation.
Question 4 (17 marks)
A manufacturer assembles television sets. If the television sets are priced at £1,000 each, the
company will sell 30 units per week, and if the television sets are priced at £800 each the sales will
be 50 units per week. The fixed weekly costs are £10,000 per week and the variable costs are £600
per unit sold. Assuming there is a linear relation between sold items and their prices, determine:
1) The price function (7 marks)
2) The weekly revenue function, and the cost function. (4 marks)
3) The manufacturer’s weekly profit function. (2 marks)
4) The breakeven point. (4 marks)
(end of assessment – formula sheet on next page)
JV804 FORMULA SHEET.
Median and quartiles:
x1, x2, …, xn is a series of observations in increasing order. The median (Q2) and quartiles (Q1 and
Q3) are:
th
?(n+1)?
Q1 = ?
? observation
? 4 ?
th
?(n+1)?
Q2 = ?
? observation
? 2 ?
Standardisation of variable ?? is : z =
?????
??
Confidence intervals:
•
? ? ???? ×
??
??
??
???
? + ???? ×
?µ???
??
??µ
??
z-test statistic: ?? = ??
? ??
?
Hypothesis Testing:
z=
x??
STEM
STEM =
?
n
??
???
th
?3(n+1)?
Q3 = ?
? observation
? 4 ?
Correlation:
Spearman’s Rank Correlation Coefficient:-
rs = 1 –
6?d²
??(??2 ?1)
Product Moment Correlation Coefficient:Sxy
r = ?Sxx.Syy
Sxy = ?xy –
(?x)(?y)
Sxx = ?x² –
(?x)²
Syy = ?y² –
(?y)²
??
??
??
Linear Regression: For a line y = a + bx :
b=
Sxy
Sxx
??? = a + b???
a=
(?y)
??
–b
(?x)
??

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