# Statistics

**Topics:**Normal distribution, Standard deviation, Statistical hypothesis testing

**Pages:**16 (2907 words)

**Published:**September 14, 2014

Contents

Question 13

Question 2a5

Question 2b6

Question 2c7

Question 3a8

Question 3b8

Question 3c10

Question 3d11

Question 412

Question 514

References15

Question 1

The sampling method that Mr. Kwok is using is Stratified Random Sampling Method. In this case study, Mr Kwok collected a random sample of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost. TABLE 1: Data Summaries of Three Routes

Route 1

Route 2

Route 3

Normal(88.532,5.07943)

Normal(97.1033,5.04488)

Normal(107.15,5.15367)

Summary Statistics

Mean

88.532

Std Dev

5.0794269

Std Err Mean

0.2271589

Upper 95% Mean

88.978306

Lower 95% Mean

88.085694

N

500

Sum

44266

Summary Statistics

Mean

97.103333

Std Dev

5.0448811

Std Err Mean

0.2912663

Upper 95% Mean

97.676525

Lower 95% Mean

96.530142

N

300

Sum

29131

Summary Statistics

Mean

107.15

Std Dev

5.1536687

Std Err Mean

0.3644194

Upper 95% Mean

107.86862

Lower 95% Mean

106.43138

N

200

Sum

21430

From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827. Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From the sample of 1000 flights, route 1 has 500 flights which carries a sample mean of 88.532 passengers; route 2 has 300 flights which carries a sample mean of 97.103 passengers and route 3 has 200 flights which carries a sample mean of 107.15 passengers. Hence the mean number of passengers in route 1 is lower than route 2 and route 3.

Reasons for Choosing Histogram

Histogram can be easily compared by identifying where the maximum, minimum and medium among the 3 different routes. In this case study, we would like to compute the total number of passengers for all the 3 routes and the variable that represents the number of passengers is a continuous variable and hence histogram is being used to do the comparison. It allows the inspection of the data for its underlying distribution (e.g., normal distribution), outliers and etc. It is also used to illustrate trends among two members or more on nominal or ordinal scales. The advantage of histogram is that it provides a quick visual check that the assumption of normality has been met.

Summary Preliminary Observation

Mean - According to our preliminary observations of the table above, route 1 has the greatest number of flights and passengers but it does not equate to having the highest mean as its sample size is the largest. The arithmetic mean for route 1 is 88.532, route 2 is 97.103 and route 3 is 107.15 with a sample size of 1000 flights. These results show that route 1 has the lowest mean number of passengers as compared to route 2 and route 3. Normal Distribution – From the table above, all the three routes are normally distributed as they have a bell curve shape, symmetrical and the curve is concentrated in the centre and decreases on either sides.

Standard Deviation – Dispersion is used for measuring the spread of the numerical information. The dispersion in number of passengers in Route 3 is the highest with the standard deviation of 5.154 as compared to Route 1 with the standard deviation of 5.080 and Route 2 with the standard deviation of 5.045. Although there is a slight difference, all three are small values and it indicates that the data are...

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