business statistics

Title: BUS105 Computing Assignment semester 2,2017

Name: Sushma GHISING TAMANG

Student number: 11701123

Allocated Sample:

The section 1 dataset consists of a population of 100,000 people split into 10,000 samples of size 10 the variables in the dataset are “income” and annual contribution to super, So you show the relationship between the variables graphically using a scatterplot and regression. You need to suppose that someone wants to predict the contribution of a person with income $200,000.

The scatter plot below shows the relationship between the variables

income” and “annual contribution to savings” for 100,000 people so 100,000 points

Using the whole population all 100,000 points the regression line is predicted annual contribution y=0.1351*x+181.2 so if the predicted annual contribution is 0.1351*200,000+181.2=27201.2

the z score (27201.2-27000)/2100= 0.0958

using wolfram alpha P(Z<0958) = 0.53816

So, if we compare 10,000 samples then expected rank will be

Predicted rank = P (Z<0958) *10000=0.53816*10,000=5381.6

Section 2

The variables mentioned are risk level (r or s), where “r” refers to the risky investment plan and ‘s’ refers to safer investment plan

sample	173
Count of made a loss (L or P)?	Column Labels
Row Labels	L	P	Grand Total
r	14	50	64
s	4	32	36
Grand Total	18	82	100
sample	173
Count of made a loss (L or P)?	Column Labels
Row Labels	L	P	Grand Total
r	21.88%	78.13%	100.00%
s	11.11%	88.89%	100.00%
Grand Total	18.00%	82.00%	100.00%

From the result we got in the above table, the loss of r is 21.88% which is more than comparing of s (11.11%) and similarly r has less profit than s(88.89%) which is 78.13%.

So the difference in proportions is -=0.2188-0.1111-=0.1077

So the zscore for that estimate is (0.1077-0.1)/0.0743= 0.1036

P(Z<zscore) = P(Z<-0.1036) = 0.541257

IF there was a list of 4000 estimates ranked from lowest to highest, the expected rank will be expected rank = P(Z<zscore)*4000= 0.541257*4000=2165.028

Section 3

sample	173
Row Labels	Count of High risk ?	Average of return	StdDev of return
n	70	0.034585714	0.003196433
y	30	0.054333333	0.098319793
Grand Total	100	0.04051	0.054051135

Comments:

As compared to y, n has the high count of risk. Average of return for y is higher than n and standard deviation is also higher for y than n.

So the difference in the sample means =0.0345-0.0543=-0.0198

The zscore of this estimate =(-0.0198- -0.0256)/ 0.0173= 0.3352

using wolframalpha.com P(Z<zscore) = P(Z<0.3352)=0.631263

If there was a list of 2000 estimates ranked from lowest to highest, what rank do you think your would be close to, hint just use the formula expected rank = P(Z<zscore)*2000= 0.631263*2000=1262.526

sample	173
Row Labels	Count of High risk ?	Average of return	StdDev of return
n	70	0.034585714	0.003196433
y	30	0.054333333	0.098319793
Grand Total	100	0.04051	0.054051135

sample	173
Row Labels	Count of do you support proposed change?
no	74
yes	138
Grand Total	212

Section 4

population proportion of people that say yes is p=120,000/200,000=0.6

Sample proportion of people that say yes is =138/212 =0.6509

So the zscore =(0.6509-0.6)/0.0357=-1.4257

P(Z<zscore)=P(Z<1.4257)=0.9230 So if we compare sample 700 to the 1000 other estimates then we expect the rank to be 0.9230*1000=923

Section 5

The data set is as shown in figure 1 below

Motorcycle Brand	Number in Stock	Average Price	Country of Origin
Yamaha	25	$10,020	Japan
BMW	45	$12,000	Germany
Ducati	77	$23,000	Italy
Honda	24	$9,000	Japan
Suzuki	75	$8,500	Japan
Kawasaki	56	$7,200	Japan

The 2 variable pivot table is as below

Row Labels	Sum of Number in Stock
BMW	45
Ducati	77
Honda	24
Kawasaki	56
Suzuki	75
Yamaha	25
Grand Total	302

The pivot table gives a summary of data presented in the table with options to truncate what data is to be viewed and which data to leave out. With a more advanced pivot table, the data can be grouped according to the country of origin of the bikes. This feature can be used to organize a large amount of data in excel automatically and prepare the data for presentation.

Section 6: Discussion

The student’s assignment from 2015 brings to perspective the usefulness of statistics in business. It highlights that it allows the business to get an idea of what people think of a business’ product with regard to market research in order to best develop a product before launching it. The student begins by introducing data collection methods but immediately focuses on taste tests as conducted in Sidney with the use of taste booths and surveys filled out during the exercise.

The study seeks to get information on the preferred version of a snack, the gender that likes it more, if they actually like the product, how much they would pay for the product, their ages, if the product meets their taste needs and if the product comes off as a salty or sweet snack. The researcher introduces a quote by Driskell that says, “the main difference between men and women when it comes to snacks is that women are likely to eat due to stress, while men are less interested in the nutritional information.”

In section 3, he begins to present the data collected in two way tables. He first shows results of how males and females like or hate the product. Presenting this also in a graphical chart, the researcher notes that more males like the product than females. A hypothesis test is conducted to check if the relationship between gender and liking or disliking the product. For this, the researcher checks if the variables are dependent. The test confirms that there is no strong evidence that the variables are dependent thus nullifying Driskell’s quote. A similar test is conducted on the relationship between gender and the amount they would pay for the product, and at this point, confidence intervals are used as well. In conclusion, the report demonstrates how numbers and figures can be used to summarise information and give insight to the business

annual contribution 174470.0 207270.0 196590.0 190910.0 150700.0 239840.0 263450.0 240160.0 194140.0 83170.0 21808.8 35857.7 28309.0 28063.8 15522.1 21825.4 37409.9 32901.9 27373.7 11311.1