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SULIT (EQT 271) SULIT - 2 -
Question 1 Soalan 1
Answer the following statements, either TRUE
or FALSE
. If it is FALSE, write the correct statement. [Jawab pernyatan-pernyataan berikut sama ada BETUL atau SALAH
. Jika SALAH, tuliskan pernyataan yang betul.] (a) When we test for differences between the means of 2 independent populations, we can only use a two-tailed test. [Apabila kita menguji perbezaan antara dua populasi min yang tidak bersandar, kita hanya boleh menggunakan ujian dua-hala.] (b) The least square regression line is the line which has the smallest of the squared residuals of any line through the data values. [Garis regresi kuasa dua terkecil ialah garis yang mempunyai kuasa dua reja terkecil bagi sebarang garis yang melalui nilai-nilai cerapan.] (c) The confidence interval obtained will always correctly estimate the population parameter. [Selang keyakinan yang diperoleh bagi menganggar parameter populasi akan selalunya betul.] (d) If the coefficient of determination is a positive value, then the regression equation could have a positive slope. [Jika pekali penentu bernilai positif, maka persamaan regresi mempunyai kecerunan yang positif.] (e) In regression analysis, the residual represent the difference between the actual Y
and the mean of Y
. [Dalam analisis regresi, reja mewakili beza antara nilai sebenar Y dan min bagi Y.] (f) ANOVA uses between groups variance measure to describe the mean difference between all groups. [ANOVA menggunakan pengukur varians antara kumpulan-kumpulan bagi menerangkan beza antara kesemua kumpulan.] (g) The least squares technique minimizes the sum of the squares of the vertical distances between actual Y
values and predicted values of Y. [Kaedah kuasa dua terkecil meminimumkan jumlah kuasa dua bagi jarak menegak antara nilai Y yang sebenar dan nilai jangkaan bagi Y.] ….
3/-
SULIT (EQT 271) SULIT - 3 -
(h) The treatment effect in ANOVA is found in the differences between group means.
[Kesan rawatan dalam ANOVA diperoleh melalui beza antara beberapa min kumpulan.] (i) When a blocking effect is included in an ANOVA, the result is a larger sum of squares error. [Apabila kesan blok dimasukkan dalam ANOVA, keputusannya adalah jumlah kuasa dua ralat yang lebih besar.] (j) Kruskal-Wallis test is the non-parametric test equivalent to the test for randomized block design. [Ujian Kruskal-Wallis adalah ujian tidak-berparameter yang bersamaan dengan ujian rekabentuk blok rawak.] (10 Marks / Markah
) ….
4/-
SULIT (EQT 271) SULIT - 4 -
Question 2 Soalan 2 A group of researchers claims that there is a difference in the mean number of car users (PRODA, PROTO and TROYOTA) which randomly selected from five (5) different locations. Assumed that the population variances are all NOT equal. Answer all of the following questions. [Sekumpulan penyelidik mendakwa terdapat perbezaan pada min bilangan pengguna kereta (PRODA, PROTO dan TROYOTA) yang dipilih secara rawak daripada lima (5) lokasi yang berbeza. Anggap kesemua populasi varians adalah TIDAK sama. Jawab semua soalan-soalan berikut.]
Table 2.1 : Number of Car Users for Each Brand of Cars [Jadual 2.1 : Bilangan Pengguna Kereta Bagi Setiap Jenama Kereta]
Location 1 Location 2 Location 3 Location 4 Location 5 PRODA 50 63 54 55 48 PROTO 66 70 50 75 64 TROYOTA 78 89 56 68 93 Table 2.2 : Summary Statistics [Jadual 2.2 : Ringkasan Statistik]
Mean,
y
Variance,
2
s
Grand Mean,
Y
PRODA 54.0 33.5 65.27 PROTO 65.0 88.0 TROYOTA 76.8 230.7 (a)
The three samples data are dependent or independent? State your reason. [Ketiga-tiga sampel data adalah bersandar atau tidak bersandar? Nyatakan sebab anda.] (2 Marks / Markah
) (b)
Formulate a suitable 0
H
and 1
H
to test the researchers claim. [Bentukkan 0
H
dan 1
H
yang bersesuaian untuk menguji dakwaan para penyelidik.]
(1 Mark / Markah
) (c)
Based on Table 2.2, [Berdasarkan Jadual 2.2,] (i)
Fill in the ANOVA table below. [Isikan jadual ANOVA di bawah.] (5 Marks / Markah
) ….
5/- Source of Variation Degree of Freedom SS MS F-statistic A 2 C E G B 12 D F TOTAL 14
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SULIT (EQT 271) SULIT - 5 -
(ii) Based on c(i), test the hypotheses in (b) at 0.05
and state your conclusion. [Berdasarkan c(i), uji hipotesis di (b) pada 0.05
dan nyatakan kesimpulan anda.]
(2 Marks / Markah
) (d)
Do the boxplots in Figure 2.1 support your conclusion in (c)(ii). State your reason. Why does the TROYOTA sample data gives the largest variation? [A
dakah ‘boxplots’ di Rajah 2.1 menyokong kesimpulan anda di (c)(ii). Nyatakan sebab anda. Mengapakah sampel data dari TROYOTA mempunyai variasi yang lebih tinggi?] Figure 2.1 : Boxplots of PRODA, PROTO, TROYOTA [Rajah 2.1 : ‘Boxplot’
bagi PRODA, PROTO, TROYOTA] TROYOTA
PROTO
PRODA
90
80
70
60
50
Number of Car Users
(2 Marks / Markah
) (e)
Based on Table 2.2 and Table 2.3, [Berdasarkan Jadual 2.2 dan Jadual 2.3,]
Table 2.3 [Jadual 2.3] Difference 95% Confidence Interval PRODA
PROTO
(-24.69, 2.69) PRODA
TROYOTA
(
R
, S
) PROTO
TROYOTA
(-33.97, 10.73) (i)
Calculate the value of R
and S
. [Kira nilai bagi R
dan S
.] (3 Marks / Markah
)
(ii)
Which pair(s) of groups has (have) no significance difference? State your reason. [Kumpulan manakah yang tidak mempunyai perbezaan yang signifikan?Nyatakan sebab anda.] (2 Marks / Markah
) (iii)
Which pair(s) of groups has (have) significance difference? State your reason. [Kumpulan manakah yang mempunyai perbezaan yang signifikan?Nyatakan sebab anda.] (2 Marks / Markah
) ….
6/
SULIT (EQT 271) SULIT - 6 -
(f)
Based on your answer in (e)(iii), verify the alternative hypothesis in (b) in order to support the researchers claim that at least one of the population mean is not equal from the others. Use 0.05.
[Berdasarkan jawapan anda di (e)(iii), sahkan hipotesis alternatif di (b) bagi menyokong dakwaan para penyelidik bahawa sekurang-kurangnya satu min populasi adalah berbeza daripada yang lain. Guna .
0.05
]
(4 Marks / Markah
) (g)
When you perform statistical test in (f), you use 5% significance level
0.05
. How do you explain 5% significance level? If you increase the significance level, do you expect the conclusion would be the same? State your reason. [Apabila anda melakukan ujian statistik di (f), anda menggunakan 5% aras keertian
0.05 .
Bagaimanakah anda menerangkan 5% aras keertian ini? Jika aras keertian meningkat, adakah anda menjangkakan kesimpulan yang sama? Berikan sebab anda.] (2 Marks / Markah
) ….
7/-
SULIT (EQT 271) SULIT - 7 -
Question 3 Soalan 3
Employees of MNM Corporation are about to undergo a retraining program. The management is trying to determine which of the three (3) programs is the best. They believe that the effectiveness of the programs may be influenced by gender. Table 3.1 shows the number of participants by gender for each program. [Kakitangan MNM Corporation akan menjalani program latihan semula. Pihak pengurusan cuba untuk menentukan satu daripada tiga (3) program manakah yang terbaik. Mereka percaya bahawa keberkesanan program mungkin dipengaruhi oleh jantina. Jadual 3.1 menunjukkan bilangan peserta bagi setiap program mengikut jantina.] Table 3.1 [Jadual 3.1]
Factor A : Program Factor B : Gender Male Female Program 1 32 24 38 30 Program 2 16 18 24 21 Program 3 30 29 36 38 A statistical software package gave the result: SS(Total) = 614.00. [Satu pakej perisian statistik memberikan keputusan ini: SS(Total) = 614.00.] (a)
Identify the suitable design for the above situation. Give your reason. [Kenal pasti rekabentuk yang sesuai untuk situasi di atas. Berikan alasan anda.] (2 Marks / Markah
) (b)
Sketch and interpret the interaction plot for the above data. [Lakar dan terangkan plot interaksi bagi data di atas.]
(4 Marks / Markah
) (c)
Construct an ANOVA table for the above data. (Use two decimal places)
[Bina jadual ANOVA bagi data di atas. (Gunakan dua titik perpuluhan)]
(10 Marks / Markah
) (d)
Based on (c), test the hypothesis at 0.01
whether there is: [Berdasarkan (c), uji hipotesis pada 0.01
sama ada terdapat:] (i)
an interaction effect between factor A and factor B on the program effectiveness? [kesan interaksi antara faktor A dengan faktor B terhadap keberkesanan program?] (3 Marks / Markah
) (ii)
an effect of factor A and factor B on the program effectiveness? [kesan faktor A dan kesan faktor B terhadap keberkesanan program?] (4 Marks / Markah
) (e)
Based on your results in (b) and (d), what would you advice to the MNM Corporation regarding the best program? Explain. [Berdasarkan jawapan anda di (b) dan (d), apakah nasihat yang dapat diberikan kepada MNM Corporation mengenai program yang terbaik? Jelaskan.] (2 Marks / Markah
) ….
8/-
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SULIT (EQT 271) SULIT - 8 -
Question 4 Soalan 4
A study is conducted by Institute of Engineering Mathematic in order to investigate if there is any correlation in students
’ performance for
Engineering and Calculus subject and their statistical knowledge. Fifteen (15) students are randomly selected and their exam scores for Calculus, Engineering and Statistics sujects are recorded. The scatterplots and regression models for data recorded are given by Figure 4.1 and 4.2. [Satu kajian dijalankan oleh Institut Matematik Kejuruteraan bagi mengkaji sama ada terdapat korelasi antara prestasi pelajar bagi subjek Kejuruteraan dan Kalkulus dengan pengetahuan statistik. Lima belas (15) pelajar dipilih secara rawak dan skor peperiksaan bagi subjek Kalkulus, Kejuruteraan dan Statistik direkodkan. Plot serakan dan model regresi bagi data yang direkodkan diberikan oleh Rajah 4.1 dan Rajah 4.2.] Figure 4.1 : Engineering versus Statistics [Rajah 4.1 : Kejuruteraan lawan Statistik] 85
80
75
70
65
60
55
85
80
75
70
65
60
Statistics
Engineering
1
1
2
ˆ
69%,
0.1359
r
s
Figure 4.2 : Calculus versus Statistics [Rajah 4.2 : Kalkulus lawan Statistik] 85
80
75
70
65
60
55
80
75
70
65
60
55
Statistics
Calculus
1
2
ˆ
2
4.3%,
0.2547
r
s
(i)
Explain the difference between correlation and regression. [Terangkan perbezaan antara korelasi dan regresi?]
(2 Marks / Markah
) (ii)
Based on Figure 4.1 and 4.2, what type of relation exists between the variables? [Berdasarkan Rajah 4.1 dan 4.2, apakah bentuk hubungan yang wujud di antara kedua-dua pembolehubah?] (2 Marks / Markah
) (iii)
Is there any significant linear relationship between Engineering and Statistics? Perform a hypothesis test at 5% significance level. [Adakah terdapat hubungan linear yang signifikan antara subjek Kejuruteraan dan Statistik? Jalankan ujian hipotesis pada aras keertian 5%.] (5 Marks / Markah
) (iv)
Interpret the slope and coefficient of determination in Figure 4.1. [Jelaskan kecerunan dan pekali penentu di Rajah 4.1.]
(3 Marks / Markah
) ….
9/- ˆ
23.3
0.731
E
S
y
x
ˆ
54.4
0.194
C
S
y
x
SULIT (EQT 271) SULIT - 9 -
(v)
What would you expect the F
-statistic for the relationship between Calculus and Statistics? Give your reason. [Apakah yang anda jangkakan F-statistik bagi hubungan antara Kalkulus dan Statistik? Nyatakan sebab anda.] (2 Marks / Markah
) (vi)
Why it is important to construct a scatterplot and perform a hypothesis test when you want to fit a linear regression model? [Mengapakah ianya penting untuk melakarkan plot serakan dan menjalankan ujian hipotesis apabila anda mahu membina model regresi linear?] (2 Marks / Markah
) (vii)
Explain the importance of statistical knowledge in Engineering course as compared to Calculus. [Terangkan kepentingan pengetahuan statistik terhadap subjek Kejuruteraan berbanding Kalkulus.] (2 Marks / Markah
) ….
10/-
SULIT (EQT 271) SULIT - 10 -
Question 5 Soalan 5 (a)
Sign Test, Mann-Whitney Test and Kruskal-Wallis Test are three types of non-parametric test. [Ujian Bertanda, Ujian ‘Mann
-
Whitney’ dan Ujian ‘Kruskal
-
Wallis’ adalah tiga jenis ujian tak-berparameter.] (i)
What is the common assumption required for the above statistical tests? In short, explain how you understand the assumption. [Apakah andaian umum yang diperlukan bagi kesemua ujian statistik di atas? Dengan ringkas, terangkan bagaimana anda memahami andaian tersebut.] (3 Marks / Markah
) (ii)
Create a suitable application for each of the test to compare the difference between the three statistical tests.
[Bina satu aplikasi yang bersesuaian bagi setiap ujian tersebut untuk membandingkan perbezaan antara ketiga-tiga ujian statistik tersebut.] (6 Marks / Markah
) (b)
AMN Engineering Sdn. Bhd. wants to increase the productivity of its line workers. Program A was applied to the current workers. You as the quality engineer proposed a new program (Program B) in order to increase the productivity. Sixteen (16) employees are randomly assigned to one of the programs. Their output in a certain day has been recorded in Table 5.1. [AMN Engineering Sdn. Bhd. ingin meningkatkan produktiviti bagi pekerja-pekerjanya. Program A telah diterapkan kepada pekerja semasa. Anda sebagai jurutera kualiti mencadangkan satu program baru (Program B) untuk meningkatkan produktiviti. Enam belas (16) pekerja telah dipilih secara rawak untuk mengikuti salah satu daripada program tersebut. Output bagi setiap pekerja pada satu hari tertentu telah direkodkan di Jadual 5.1.] Table 5.1 [Jadual 5.1] Program A Program B 150 110 160 185 180 180 135 130 120 220 160 210 135 145 150 155 (i)
Based on Table 5.1, suggest which program is more productive? State your reason. [Berdasarkan Jadual 5.1, cadangkan program yang lebih produktif? Nyatakan sebab anda.]
(4 Marks / Markah
) (ii)
You want to know whether the new program B is more productive than program A by using a non-parametric test. Suggest the appropriate statistical test. Is there any evidence to support your hypothesis? Test at 0.05.
[Anda ingin mengetahui sama ada program baru B adalah lebih produktif berbanding program A dengan menggunakan ujian tak-berparameter. Cadangkan ujian statistik yang sesuai. Adakah bukti yang mencukupi bagi menyokong hipotesis anda? Uji pada 0.05.
]
(9 Marks / Markah
) ooOooo
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2
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- Base on the same given data uploaded in module 4, will you conclude that the number of bathroom of houses is a significant factor for house price? I your answer is affirmative, you need to explain how the number of bathroom influences the house price, using a post hoc procedure. (Please treat number of bathrooms as a categorical variable in this analysis) Base on the same given data, conduct an analysis for the variable sale price to see if sale price is influenced by living area. Summarize your finding including all regular steps for your method. Also, will you conclude that larger house corresponding to higher price (justify)?arrow_forwardHere is the headline of an MPR news story, "MPR News/Star Tribune poll: 56 percent approve of Walz performance" Tim Pugmire | MPR News Feb 25, 2020. This story is from before the current COVID-19 crisis and we don't know how much opinions might have changed recently. A new MPR News/Star Tribune Minnesota Poll shows 56 percent of those surveyed said they approve of his job performance, 25 percent disapprove and 19 percent are unsure. The poll of 800 registered voters was conducted by Mason-Dixon Polling and Strategy from Feb. 17-19. There were at least six other questions asked in the poll, ranging from questions on spending priorities to questions on mining and marijuana legalization. Since there are many questions asked in the poll, we don't construct several confidence interval estimates for each proportion, we calculate the sample proportions and report one margin of error for the entire poll or survey. What margin of error would you report for this poll? Use a confidence level of…arrow_forwardHere is the headline of an MPR news story, "MPR News/Star Tribune poll: 56 percent approve of Walz performance" Tim Pugmire | MPR News Feb 25, 2020. This story is from before the current COVID-19 crisis and we don't know how much opinions might have changed recently. A new MPR News/Star Tribune Minnesota Poll shows 56 percent of those surveyed said they approve of his job performance, 25 percent disapprove and 19 percent are unsure. The poll of 800 registered voters was conducted by Mason-Dixon Polling and Strategy from Feb. 17-19. There were at least six other questions asked in the poll, ranging from questions on spending priorities to questions on mining and marijuana legalization. Since there are many questions asked in the poll, we don't construct several confidence interval estimates for each proportion, we calculate the sample proportions and report one margin of error for the entire poll or survey. Choose the best response below for what the "margin of error" means. O It is a…arrow_forward
- &:!&:!&,’vdnnsinidmvkdmvkdmvkdmcarrow_forwardWhat is Stem and Leaf Display?arrow_forwardA professor believes that people learn better when they are taught in an active rather than passive fashion. To test this, he teaches a group of students from the CJBS subject pool a lesson and then gives them a test. Half of the subjects are taught by listening to a lecture, the other half are taught by having them complete work sheets. a) What is/are the independent variable(s)? Is each one a true independent variable or a subject variable? b) How many levels are there for each I.V.? What are they? c) What is/are the dependent variable(s)? How is it measured or operationalized?arrow_forward
- agtataya) Puzzled! complete the Cross Quantile Puzzle by finding the specified measures of position. Use linear interpolation. In filling the boxes, disregard the decimal point. For example, 14.3 should be written as 1 4 3 I already answered number 1 to serve as your guide. Use the space provided and also the back of this page to show your solution. Problem: The following are the scores of a random sample of twelve students: 5, 7, 25, 30, 36, 42, 14, 12, 15, 22, 53, 65. 2 Across Down 3 2. D7 1. Q2 35(n+1) 3. 4. Q3 100 8. 62(n+1) 5. P40 100 11 6. Ps2 8 9. P35 7. P54 10. IQR 11. Q1 10 Solution: 1. Find Q2. Step 1: Arrange the data set from smallest to largest 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65 Step 2: Compute the position of the quartile 12(50) nk 600 = 6 %3D 100 100 Step 3: Since c= 6 (whole number), tingnan ang numero na nasa ika-anim na pwesto tapos idagdag ang kasunod na numero at panghuli ay i-divide sa 2 para makuha ang kabuuan. 22+25 100 47 = 23.5 2 2 It should be…arrow_forwardA testing service makes an error that causes all the SAT scores for several thousand students to be low by 58 points. Which statement is true? Group of answer choices A) All the scores had the same relative error, but the absolute errors varied. The percentage was the same, but the difference between the measurement and the true value varied. B) All the scores had the same relative error, but the absolute errors varied. If all of the scores have the same relative error, then they will be the same amount of points less than the actual score. C) All the scores had the same absolute error, but the relative errors varied. The relative error for any given score will be that score divided by 58. D) Both the absolute and relative errors were the same in all cases because the same error is made for each score.arrow_forwardA testing service makes an error that causes all the SAT scores for several thousand students to be low by 58 points. Which statement is true? Group of answer choices A) All the scores had the same relative error, but the absolute errors varied. The percentage was the same, but the difference between the measurement and the true value varied. B) All the scores had the same relative error, but the absolute errors varied. If all of the scores have the same relative error, then they will be the same amount of points less than the actual score. C) All the scores had the same absolute error, but the relative errors varied. The relative error for any given score will be that score divided by 58. D) All the scores had the same absolute error, but the relative errors varied. If all of the scores have the same absolute error, then they will be that many points off from the true value of the exam score. E) Both the absolute and relative errors were the same in all cases because…arrow_forward
- Do American’s views of the war in Iraq vary by religion?A study conducted in 2007 by The Baylor Department ofSociology asked, “Was going to Iraq the right decision?”The table summarizes responses from a 1571 randomlyselected adults. a) What percentage of respondents agreed that going toIraq was the right thing to do? b) What percentage of respondents classified their reli-gion as “None” and agreed that the war in Iraq was the right decision?c) What percentage of the respondents who classifiedtheir religion as “None” agreed that the war in Iraqwas the right decision?d) What percentage of the respondents who agreed thatthe war in Iraq was the right thing to do classifiedtheir religion as “None”?e) Were respondents’ opinions about the war in Iraqindependent of whether or not they were religious?Justify your decision using your answers from 2 ofthe prior questions.f) Among the respondents who identified a religion, wasthere an association between the religious affiliationand opinion about…arrow_forwardA researcher wants to determine the average amount of minutes it takes for a medicine to reduce headache pain for adult males. The researcher contacted 114 subjects to participate in the study, but only got results from 84 of the subjects. The average time it took for the medicine to reduce headache pain for these subjects was 19 minutes. What is the population? Males 114 adult males Adult males 19 adult males Adult females Females 84 adult males What is the sample? Females Males 19 adult males 84 adult males Adult females Adult males 114 adult males What is the parameter? 114 people The average time that it takes for this medicine to reduce pain in adult males. The average time that it takes for this medicine to reduce pain for these 84 adult males. 84 people The average time that it takes for this medicine to reduce pain. 19 minutes What is the symbol for this parameter? S σσ P xˉx̄ μμ pˆp̂ What is the statistics? The average time that it takes for this…arrow_forwardThe overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. Brand 1: 275, 286, 287, 271, 283, 271, 279, 275, 263, 267 Brand 2: 258, 244, 260, 265, 273, 281, 271, 270, 263, 268 a) Is there evidence to support the claim that the standard deviation of overall distance is the same for both brands of balls (use α = 0.05)? b) Is there evidence to support the claim that the mean of the overall distance is the same for both brands of balls (use α = 0.05)?arrow_forward
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