Statprob Final Assignment 2015-Revision

7/24/2019 Statprob Final Assignment 2015-Revision

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FINAL ASSIGNMENT

STATISTICS AND PROBABILITY

Raihan Alisha Nabila 1306437126

Talitha Jauza Utami 1306387134

R A Tamara RF Iskandar 1306388894

Rafitya Rahisa 1306437063


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UNIVERSITY OF INDONESIA

FACULTY OF ENGINEERING

CIVIL ENGINEERINGINTERNATIONAL PROGRAM

A. TOPIC

Inferential and Descriptive Statistics

B. PROBLEM DESCRIPTION

The data are collected from the number of visitors every 10 minutes in both coffee

shops of Starbucks and J.CO, those are located in Pondok Indah Mall 1, South

Jakarta. Then, these data are calculated and discussed statistically by our group. From the

result of the collected data we would like to know if the average and the variance number

of visitors of these two different coffee shops are the same.

C. COLLECTING DATA

C.1. Type of Sample : Probability SampleSimple Random Sample

C.2. Collecting Sample Method : Observation of Visitors in 2 Coffee shops

C.3. Period of Collecting Sample : May, 3rd 2015

C.4. Number of Sample : 60 Samples


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D. RAW DATA

Every 10

minute(s)

Time Starbucks J.CO

Visitor(s)

1 12.00 12.10 8 9

2 12.10 12.20 11 83 12.20 12.30 13 8

4 12.30 12.40 5 8

5 12.40 12.50 18 17

6 12.50 13.00 8 4

7 14.00 14.10 21 25

8 14.10 14.20 11 13

9 14.20 14.30 11 13

10 14.30 14.40 15 8

11 14.40 14.50 20 8

12 14.50 15.00 13 1013 16.00 16.10 6 8

14 16.10 16.20 19 14

15 16.20 16.30 5 10

16 16.30 16.40 6 3

17 16.40 16.50 7 4

18 16.50 17.00 10 12

19 17.00 17.10 15 17

20 17.10 17.20 14 13

21 17.20 17.30 20 15

22 17.30 17.40 16 1623 17.40 17.50 18 17

24 17.50 18.00 15 20

25 19.00 19.10 8 10

26 19.10 19.20 12 15

27 19.20 19.30 20 15

28 19.30 19.40 17 10

29 19.40 19.50 10 18

30 19.50 20.00 10 11

Table 1 . Data of The Number of visitors every 10 minutes in Starbucks and Jco Pondok Indah Mall


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E. DISTRIBUTION FUNCTION AND HISTOGRAM

1. Starbucks Pondok Indah Mall 1

VisitorRange

Frequency

0 - 5 2

6 - 10 9

11 - 15 10

16 - 20 8

21 - 25 1

Total 30

Table 2. Frequency of visitors in Starbucks PIM 1

Graph 1 . Histogram of visitors in Starbucks PIM 1

0

2

4

6

8

10

12

0 - 5 6 - 10 11 - 15 16 - 20 21 - 25

Frequency

Number of Visitors

The number of Starbucks Coffee visitors

every 10 minutes

Frequency


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2. J.CO Pondok Indah Mall 1

Visitor Range Frequency0 - 5 3

6 - 10 11

11 - 15 9

16 - 20 6

21 - 25 1

Total 30

Table 3. Frequency of visitors in J.CO PIM 1

Graph 2 . Histogram of visitors in J.CO PIM 1

0

2

4

6

8

10

12

0 - 5 6 - 10 11 - 15 16 - 20 21 - 25

Frequency

Number of Visitors

Histogram

Frequency


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F. Descriptive Statistic

Starbucks Pondok Indah Mall 1 J.CO Pondok Indah Mall 1

Mean 12.73333333 Mean 11.96666667

Standard Error 0.903293251 Standard Error 0.912849943

Median 12.5 Median 11.5

Mode 8 Mode 8

Standard Deviation 4.947540896 Standard Deviation 4.999885056

Sample Variance 24.47816092 Sample Variance 24.99885057

Kurtosis -1.164701437 Kurtosis 0.257040297

Skewness 0.0867804 Skewness 0.393573284

Range 16 Range 22

Minimum 5 Minimum 3

Maximum 21 Maximum 25

Sum 382 Sum 359

Count 30 Count 30

Confidence Level(95.0%) 1.847442133 Confidence Level(95.0%) 1.866987763

Table 3 . Descriptive Statistic of Starbucks PIM Table 4. Descriptive Statistic of J.CO PIM


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G. PROBABILITY AND CUMMULATIVE DISTRIBUTION FUNCTION

1. Starbucks PIM 1

X Frequency PDF CDF

5 2 0.023768 0.059019

6 2 0.031939 0.086765

7 1 0.041202 0.123264

8 3 0.051023 0.169358

10 3 0.069222 0.290316

11 3 0.075835 0.363041

12 1 0.079754 0.441084

13 2 0.080517 0.521492

14 1 0.078035 0.601032

15 3 0.072601 0.67657416 1 0.064842 0.745457

17 1 0.055594 0.805761

18 2 0.045757 0.856449

19 1 0.036153 0.897355

20 3 0.027421 0.929049

21 1 0.019966 0.952626

Total f 30

STDV 4.9475409

MEAN 12.733333

Table 5 . Probability Density Function and Cumulative Density Function of Starbucks PIM

Graph 3 . PDF of Starbucks PIM 1

0

0.05

0.1

0 5 10 15 20 25

Probability

Number of visitors every 10 minutes

Probability Density Function of

Starbucks PIM 1

PDF


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Graph 4 . CDF of Starbucks PIM 1

Graph 5. PDF and CDF of Starbucks PIM 1

0

0.5

1

1.5

0 5 10 15 20 25

Probability


Cumulative Density Function of

Starbucks PIM 1

CDF

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Probability

Numbr of Visitors Every 10 Minutes

PDF and CDF of Starbucks PIM 1

PDF

CDF


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2. J.CO PIM 1

X frequency pdf cdf

3 1 0.015979 0.036456

4 2 0.022421 0.055539

8 6 0.058247 0.2137869 1 0.066912 0.276474

10 4 0.07385 0.347033

11 1 0.078313 0.423347

12 1 0.079789 0.502659

13 3 0.078104 0.581867

14 1 0.073458 0.657877

15 3 0.066378 0.727968

16 1 0.057629 0.790076

17 3 0.048072 0.842958

18 1 0.038527 0.886225

20 1 0.021948 0.94594

25 1 0.00267 0.995429

total

frequency

30

stdv 4.999885

mean 11.96667

Table 6 . PDF and CDF of J.CO PIM 1

Graph 6 . PDF of J.CO PIM 1

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20 25 30

Probability

number of visitors every 10 minutes

Probability Density Function of J.CO

PIM 1

pdf


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Graph 7 . CDF of J.CO PIM 1

Graph 8 . PDF and CDF of J.CO PIM 1

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30

Probability


Cumulative Density Function of J.CO

PIM 1

cdf

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

P

robability

Number of Visitors Every 10 Minutes

PDF and CDF of J.CO PIM 1

pdf

cdf


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H. HYPOTHETICAL TEST

Hypothesis (Ho): The average number of visitors of Starbucks Coffee and is the same with

the level of significant is 0.05.

1. H0: 1= 2

H1: 1 2

2. = 0,05

3. Uses z distribution because n = 60 > 30

4. Boundaries for acceptance/rejection critical points : : /2 = 0.025. From z-score table, the

boundaries are Z0,025= +1.960.

5. Decision : Reject H0and accept H1 when RUz< -1.960 or RUz> +1.960. If not, accept H0.

6. Ratio test :

Using the average of the number of visitors

x1-x2 = +=

4.9530 + 4.9930 = 0.5756

RUz= ztest=-x1-x2

=12.7311.967

0.5756 = 1.32557 > -1.960

Using the variance of the number of visitors

x1-x2 = +=

24.4830 + 2530= 1.28

RUz= ztest=

-x1-x2 =

12.7311.9671.28 = 0.596 > -1.960


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7. Decision Making:

Because RUz is between >-1.960 which means in between 1.960, so H0is

accepted. That means the average number of visitors at Starbucks Coffee Pondok Indah

Mall 1 equalsto the average number of visitors at Pondok Indah Mall 1 and the variance

number of visitors at at Starbucks Coffee Pondok Indah Mall 1 equalsto the variance

number of visitors at Pondok Indah Mall 1 .

I. FINAL DISCUSSION

The null hypothesis (Ho) which was tested in this report was according to the number of

visitors in both coffee shops which were Starbucks Coffee and J.CO located in Pondok

Indah Mall 1, South Jakarta. We collected the data on Sunday (3rdof May 2015).We

recorded the data of the visitors every 10 minutes in both coffee shops .The level of

significance used was 0.05. Because both data are independent data, the total amount was

more than 30 and there were sample variances of both samples, we used z-distribution to

calculate the hypothesis. With the level of significance of 0.05, we got the boundaries of

critical area of 1.960 from z-score table. Based on the ratio test above, the value of RUz

that we obtained was bigger than -1.960 and less than 1.960. Therefore, we can conclude

the average and the variance number of visitors who visit Starbucks Coffee and J.CO are

the same.

Statprob Final Assignment 2015-Revision

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