STATS1900 Mock Exam Solution
Duration: 1 Hour
Answer:
P(X<10) = 0.5 P(X=10)
P(X=10) Z = (X- mu)/ st. dev = (10 -16.17)/3.03=2.0363
P(X=10) = P(Z=2.0363) = 0.4793
P(X<10) = 0.5- 0.4963 =0.0207
X = s / n = 3.03/35 =0.512
Confidence Interval = mean +- k * st. error
= 16.17 +- 2.0 *0.512 = 16.17 +- 1.024 = 15.146
to 17.194
95% time to resolve a complain it will take from 15.146 days to 17.194
days.
Null Hypothesis, H0: =200 grams
Alternative Hypothesis, H1: >200 grams
p-value = 0.103
Test-statistic value= 1.26
Since P-value is greater than 0.05 therefore accept H0. The mean
weight of the chocolate bars is less or equal to 200 grams.
The relationship between weekly sales of pet food and the shelf space
is linear and positive.
Y = b0 + b1 X
Sales= 1.45 + 0.0740 Shelf-space
Slope coefficient value= 0.0740
If the shelf-space is increased by 1 meter then weekly sales of pet food
will be increased by 0.0740 hundred dollar which is $7.40.
Sales= 1.45 + 0.0740 Shelf-space
= 1.45 + 0.0740*30
= 3.67 hundred dollar = $367
The model can predict for the self-space size from 0 meter to 25
meters, so this is not a good use of the regression equation.
t- statistic = b1/ st. error = 0.0740 /0.0159 = 4.65
R square value is large
St. error is relatively low
Both b0 and b1 is significant.
Therefore, the model is a good.
Ans:
48.7 41.2 28.3 35.6 42.8
X 39.32
5
Y 0.6 49.6 0.4 43.96 47.34
a)
B)
A: Exponentially smoothed series
B: 5PMA Raw Data
C: Raw Data
C) Trend component: Present; shown by trend line with positive slope.
Cyclic component: Present; shown by gentle up and down movement.
Seasonal component: Not present ; since data is yearly.
Irregular component: Present; shown in the variable shape of the the
hills or peaks .
Question 5:
L = Pk * Q0 / P0 * Q0 = 132.35 /86.7 =1.527 * 100 =152.7
Paasche= Pk * Qk / P0 * Qk = 160.3/104.7 =1.531 *100 = 153.10
Laspeyres index use base year quantity but Paasche index uses current
year quantity.
Question 6:
Jackie takes out a loan of $10000. She agrees to repay $4000 after 1
year and a further $3000 at the end of 2 years. If interest is charged
at a rate of 8.4% pa, payable monthly, find the amount of the final
payment which must be made at the end of 3 years in order to fully
reply the loan.
P = 10,000, i = 0.084/12= 0.007
10 ,000 4 ,000 1.007 12 3 ,000 1.007 24 X 1.007 36
0.778 X 10 ,000 3 ,678.80 2 ,537.55 3 ,783.65
X 4 ,863.30
$4,863.30
Answer: a) Quaterly, i = 2.5/400 = 0.00625
N= 4
Annual, e = (1+i)n -1
= (1+0.00625)4 -1 =0.02524 =2.524%
b) Quaterly, I = 2.8/400= 0.007
S= P(1+i)n = 15000(1+0.00625)5 =15474.65
S= P(1+i)n =15474.65(1+ 0.007)2 = 15692.05
Question 8:
N = 30*12 =360
Monthly, I = 5.25/1200 = 0.004375
N = 360 months
P = 470000 80000 = 390000
R = Pi /( 1( 1+i )n = 390000*0.004375 /( 1( 1+0.004375 )360
= 2153.59
c) Find the equity of Jamie after 22 years.
Monthly, I =0.004375
R=2153.59
N= 96 months
n
P (22 years) = R ( 1( 1+i ) )/i
96
= 2153.59( 1( 1+0.004375 ) )/0.004375
Therefore, Equity = 80000 + (loan amont P (22years)
= 80000 + (390000 P(22 years)
Table 1: The Standardized Normal Distribution
Each entry in the body of the table represents the
area under the standardized normal distribution
between the mean (z = 0) and the specified z-score.
Negative z-values refer to points on the left half of
the distribution
0
z
Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359
0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753
0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141
0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517
0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879
0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224
0.6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2518 .2549
0.7 .2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852
0.8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133
0.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389
1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621
1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830
1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015
1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177
1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319
1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441
1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545
1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633
1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706
1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767
2.0 .4772 .4778 .4783 .4788 .4793 .4898 .4803 .4808 .4812 .4817
2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857
2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4886 .4890
2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916
2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936
2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952
2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964
2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974
2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981
2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986
3.0 .49865 .49869 .49874 .49878 .49882 .49886 .49889 .49893 .49897 .49900
3.1 .49903 .49906 .49910 .49913 .49916 .49918 .49921 .49924 .49926 .49929
3.2 .49931 .49934 .49936 .49938 .49940 .49942 .49944 .49946 .49948 .49950
3.3 .49952 .49953 .49955 .49957 .49958 .49960 .49961 .49962 .49964 .49965
3.4 .49966 .49968 .49969 .49970 .49971 .49972 .49973 .49974 .49975 .49976
3.5 .49977 .49978 .49978 .49979 .49980 .49981 .49981 .49982 .49983 .49983
3.6 .49984 .49985 .49985 .49986 .49986 .49987 .49987 .49988 .49988 .49989
3.7 .49989 .49990 .49990 .49990 .49991 .49991 .49992 .49992 .49992 .49992
3.8 .49993 .49993 .49993 .49994 .49994 .49994 .49994 .49995 .49995 .49995
3.9 .49995 .49995 .49996 .49996 .49996 .49996 .49996 .49996 .49997 .49997
Table 2: Student's t-Distribution
For a particular number of degrees of freedom
each entry represents the critical value of t
corresponding to a specified upper tail area
0
t
Degree
Upper Tail Area
s of
Freedo .25 .10 .05 .025 .01 .005
m
1 1.0000 3.0777 6.3138 12.706 31.820 63.6574
2 7
2 0.8165 1.8856 2.9200 4.3027 6.9646 9.9248
3 0.7649 1.6377 2.3534 3.1824 4.5407 5.8409
4 0.7407 1.5332 2.1318 2.7764 3.7469 4.6041
5 0.7267 1.4759 2.0150 2.5706 3.3649 4.0322
6 0.7176 1.4398 1.9432 2.4469 3.1427 3.7074
7 0.7111 1.4149 1.8946 2.3646 2.9980 3.4995
8 0.7064 1.3968 1.8595 2.3060 2.8965 3.3554
9 0.7027 1.3830 1.8331 2.2622 2.8214 3.2498
10 0.6998 1.3722 1.8125 2.2281 2.7638 3.1693
11 0.6974 1.3634 1.7959 2.2010 2.7181 3.1058
12 0.6955 1.3562 1.7823 2.1788 2.6810 3.0545
13 0.6938 1.3502 1.7709 2.1604 2.6503 3.0123
14 0.6924 1.3450 1.7613 2.1448 2.6245 2.9768
15 0.6912 1.3406 1.7531 2.1315 2.6025 2.9467
16 0.6901 1.3368 1.7459 2.1199 2.5835 2.9208
17 0.6892 1.3334 1.7396 2.1098 2.5669 2.8982
18 0.6884 1.3304 1.7341 2.1009 2.5524 2.8784
19 0.6876 1.3277 1.7291 2.0930 2.5395 2.8609
20 0.6870 1.3253 1.7247 2.0860 2.5280 2.8453
21 0.6864 1.3232 1.7207 2.0796 2.5177 2.8314
22 0.6858 1.3212 1.7171 2.0739 2.5083 2.8188
23 0.6853 1.3195 1.7139 2.0687 2.4999 2.8071
24 0.6848 1.3178 1.7109 2.0639 2.4922 2.7969
25 0.6844 1.3163 1.7081 2.0595 2.4851 2.7874
26 0.6840 1.3150 1.7056 2.0555 2.4786 2.7787
27 0.6837 1.3137 1.7033 2.0518 2.4727 2.7707
28 0.6834 1.3125 1.7011 2.0484 2.4671 2.7633
29 0.6830 1.3114 1.6991 2.0452 2.4620 2.7564
30 0.6828 1.3104 1.6973 2.0423 2.4573 2.7500
40 0.6807 1.3031 1.6839 2.0211 2.4233 2.7045
50 0.6794 1.2987 1.6759 2.0086 2.4033 2.6778
60 0.6786 1.2958 1.6706 2.0003 2.3901 2.6603
70 0.6780 1.2938 1.6669 1.9944 2.3808 2.6479
80 0.6776 1.2922 1.6641 1.9901 2.3739 2.6387
90 0.6772 1.2910 1.6620 1.9867 2.3685 2.6316
100 0.6770 1.2901 1.6602 1.9840 2.3642 2.6259
0.6745 1.2816 1.6449 1.9600 2.3263 2.5758
