ELEMENTARY DATA ANALYSIS ANALISIS DATA PERMULAAN
Question 1
According
to an e-hailing operator, the average number of customers between 7am to 10am
is 11, with a variance of 3. His friend from another area does not believe that
the variance is 3. He counts the number of customers in 12 other areas and
obtained the data as in Table 1.
Table 1
|
Area |
Number of Customers |
|
1 2 3 4 5 6 7 8 9 10 11 12 |
12 11 10 9 8 13 11 10 12 8 6 10 |
a) Construct
a complete hypothesis test to test the friend’s claim at a = 0.05.
b) Based
on your answer in (a) state a brief summary of the overall variance number of
customers.
Question
2
A principal of a private school would like to know whether the median salary of parents is more than RM8000 per month. Data of salary for 10 parents is shown in Table 2.
Table 2
|
Parent |
Salary
(RM) |
|
1 2 3 4 5 6 7 8 9 10 |
7500 7000 8700 8500 9100 10000 9300 8700 7700 8500 |
a) Construct
a complete hypothesis test using sign test method to test whether the
principal’s claim is correct or not at a = 0.05.
b) Based
on your answer in (a) state a brief summary of the median salary of overall parents
for children studied in private school.
Question 3
Nutrition and sports
experts concern themselves with a person’s percentage of total body weight made
up of fat. A sport researcher interested to know if height is related to body
fat percentage. He collected a data from 10 football players as shown in Table
3.
Table 3
|
Player |
Height (cm) |
Body Fat (%) |
|
1 2 3 4 5 6 7 8 9 10 |
171 182 169 185 182 177 175 171 175 172 |
13.3 7.1 26.3 11.4 30.7 22.9 17.2 13.4 5.1 13.7 |
a)
Calculate
the Pearson correlation coefficient between height and body fat.
b)
Test
whether there exist correlation between height and body fat using a = 0.05.
c)
Based
on your answer in (a) and (b), comment the overall relationship between height
and body fat.
Soalan 1
Menurut seorang pengendali e-hailing, purata bilangan pelanggan antara
jam 7 pagi hingga 10 pagi adalah 11 orang, dengan varians 3 orang. Rakan beliau
dari kawasan lain tidak percaya bahawa varians adalah 3. Dia menghitung
bilangan pelanggan di 12 cawangan lain dan memperoleh data seperti Jadual 1.
Jadual 1
|
Kawasan |
Bilangan Pelanggan |
|
1 2 3 4 5 6 7 8 9 10 11 12 |
12 11 10 9 8 13 11 10 12 8 6 10 |
a)
Bina ujian
hipotesis lengkap untuk menguji dakwaan rakan tersebut pada a = 0.05.
b) Berdasarkan jawapan anda di (a)
nyatakan ringkasan kesimpulan mengenai keseluruhan varians bilangan pelanggan.
Soalan 2
Seorang pengetua sekolah swasta ingin mengetahui sama ada median gaji ibubapa
melebihi RM8000 sebulan. Data gaji 10 graduan baharu dipaparkan dalam Jadual 2.
Jadual 2
|
Ibubapa |
Gaji (RM) |
|
1 2 3 4 5 6 7 8 9 10 |
7500 7000 8700 8500 9100 10000 9300 8700 7700 8500 |
a) Bina ujian hipotesis lengkap menggunakan kaedah ujian
tanda untuk menguji sama ada dakwaan pengetua tersebut betul atau tidak pada a = 0.05.
b) Berdasarkan jawapan anda di (a) nyatakan ringkasan
kesimpulan median gaji keseluruhan ibubapa bagi kanak-kanak yang belajar di sekolah
swasta.
Soalan 3
Pakar pemakanan
dan sukan mementingkan peratusan berat badan seseorang yang terhasil daripada
lemak. Seorang penyelidik sukan berminat untuk mengetahui sama ada ketinggian berhubung
kait dengan peratusan lemak badan. Beliau mengumpulkan data 10 pemain bola
sepak seperti yang ditunjukkan dalam Jadual 3.
Jadual 3
|
Pemain |
Tinggi
(sm) |
Lemak
Badan (%) |
|
1 2 3 4 5 6 7 8 9 10 |
171 182 169 185 182 177 175 171 175 172 |
13.3 7.1 26.3 11.4 30.7 22.9 17.2 13.4 5.1 13.7 |
a)
Kira korelasi koefisien Pearson antara ketinggian dengan
lemak badan.
b)
Uji sama ada terdapat hubungan antara ketinggian dengan
lemak badan pada a = 0.05.
c) Berdasarkan jawapan anda di (a) dan (b), komen secara
keseluruhan hubungan antara ketinggian dengan lemak badan.
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