t chi sqr mann

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BUSINESS STATISTICSBUSINESS STATISTICS


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T statisticsT statisticsStudentsStudents Pocket money(Rs.)Pocket money(Rs.)

11 25002500

22 15001500

33 17001700

44 10001000

55 15001500

66 60060077 800800

88 700700

99 20002000

1010 800800

1111 15001500

1212 25002500

1313 20002000

1414 40004000

1515 35003500

Problem definition:Problem definition: we havewe havechosen to approximate thechosen to approximate the pocket money of 15 students pocket money of 15 studentsof our college because thisof our college because thiswas the most suitablewas the most suitablemeasurement of t statisticsmeasurement of t statisticsand was the most reliableand was the most reliabledata that could be collecteddata that could be collectedfrom the collegefrom the collegeWe have surveyed 15 people

about the pocket money theyget. The average of it was1000. Use a 5% level of significance to determine if the average is more thanwhat is quoted.


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Scale of DataScale of Data ratio ratioSamplingSampling convenient convenient- .05(because the sources of the collected data is reliable, so we did not assume a higher - .05(because the sources of the collected data is reliable, so we did not assume a higher

level of error rate)level of error rate)Justification for tool usedJustification for tool used because the sample size is less than 30 so we use the t statistics because the sample size is less than 30 so we use the t statisticsSTEP 1STEP 1 : H: H00 : = 1000 (average of pocket money of 15 people is 1000): = 1000 (average of pocket money of 15 people is 1000)

HHaa : >1000(average of pocket money is greater than 1000): >1000(average of pocket money is greater than 1000) STEP 2STEP 2 : The appropriate statistical test is: The appropriate statistical test is

t = [ - ]/(s/ n)t = [ - ]/(s/ n)STEP 3STEP 3 : - .05: - .05STEP 4STEP 4 : df = n-1: df = n-1

= 15 1= 15 1= 14.= 14.

One tail testOne tail testtc = t.05,14 = 1.761tc = t.05,14 = 1.761

decision is to reject the null hypothesis if the observed t statistics is greater than 1.761.decision is to reject the null hypothesis if the observed t statistics is greater than 1.761.Step 5Step 5 : data is as follows:: data is as follows:


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StudentsStudents Pocket money ( Rs. )Pocket money ( Rs. )

11 25002500

22 15001500

33 17001700

44 10001000

55 15001500

66 600600

77 800800

88 700700

99 20002000

1010

800800

1111 15001500

1212 25002500

1313 20002000

1414 40004000

1515 35003500

X x- x(bar)2500 528049.29

1500 74709.29

1700 5377.29

1000 598039.29

1500 74709.29

600 1376703.29

800 947371.29

700 1152037.29

2000 51379.29

800 947371.29

1500 74709.29

2500 528049.29

2000 51379.29

4000 4958059.29

3500 2981389.29

X = 26600 total= 14349333.96

Sample standard deviation is calculated as foll


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n= 15n= 15= 26600/15= 26600/15= 1773.33= 1773.33

s= [(x- x(bar))^2/n-1]s= [(x- x(bar))^2/n-1]

= (14349333.96/14)= (14349333.96/14)= 1012.399= 1012.399

STEP 6STEP 6 : t = x(bar)- / (s/n): t = x(bar)- / (s/n)= 1773.33 1000)/(1012.399/15)= 1773.33 1000)/(1012.399/15)

= 773.33/261.400= 773.33/261.400= 2.96= 2.96STEP 7STEP 7 : t: tobservedobserved > t> tcricitcalcricitcal

2.96>1.7612.96>1.761Hence, null hypothesis is rejected.Hence, null hypothesis is rejected.

STEP 8STEP 8 : Business Implication: from the data gathered we could conclude: Business Implication: from the data gathered we could concludethat the average pocket money of students of our college is greater thanthat the average pocket money of students of our college is greater than1000.1000.


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Chi square proportionChi square proportion

A total of --- 45 people are surveyed and asked if they are affected byrecession. We expect that the 60% of population says that recession hasaffected them. We wish to disprove the outcome and say that more than60% favor this. Out of 45 people, 32 said that recession has affectedthem.

Problem definition - In this time of recession, we would like to knowabout the number of people who are affected by recession. Only 60% saidthat they are affected by recession. We took a sample of 45 people fromour college, out of which 32 said that recession had affected them.Because the number of classifications is 2 so we will use chi squareproportionScale of Data NominalSampling convenient Sampling= .05Justification for tool used out of a total of 45 only 32 answeredaccording to our expectations so we need to apply the populationproportion using CHI SQUARE GOODNESS-OF-FIT TEST.


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Mann-Whitney U test(large)Mann-Whitney U test(large)Do the Vodafone users have less monthly spendingDo the Vodafone users have less monthly spendingon their mobiles as compared to reliance users? Toon their mobiles as compared to reliance users? Totest this we have selected 2 groups of people: onetest this we have selected 2 groups of people: one

who use Vodafone and other who uses reliance. Usewho use Vodafone and other who uses reliance. Usethe data and determine whether Vodafone users spendthe data and determine whether Vodafone users spendless on their mobiles than reliance customers. = .05less on their mobiles than reliance customers. = .05

Problem identificationProblem identification -if we were the management-if we were the managementof reliance(RIM) company so we would be interestedof reliance(RIM) company so we would be interestedin knowing the reason of falling of our sales asin knowing the reason of falling of our sales ascompared to that of vodafone (VF)customers. Wecompared to that of vodafone (VF)customers. Wewould also be interested in knowing that why are thewould also be interested in knowing that why are thecustomers more interested in spending on VF and notcustomers more interested in spending on VF and noton reliance?on reliance?

ScaleScale - ratio which is later converted to ordinal on- ratio which is later converted to ordinal onrankingrankingSamplingSampling convenient convenient= .05= .05

Reliance(R) Vodafone(VF)

50 150

100 130

111 250

121 222

500 345

350 551

450 345

600 650

300 700

333 850

333 222

123

Justification for tool used because the population is large (greater than 10) and the twosamples are independent of each other, so we are using the MANN WHITNEY U TEST

(LARGE)


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Step1: H0:monthly expenditure of both groups, on mobile, is equal.Ha: monthly expenditure of both groups, on mobile, is not equal.

Step 2: large sample Mann-Whitney U test is appropriate.Step 3: alpha=0.05Step 4: if the p value of sample statistics is < 0.05, decision is toreject the null hypothesis

value Rank group value Rank group

50 1 R 333 12.5 R

100 2 R 345 14.5 VF

111 3 R 345 14.5 VF

121 4 R 350 16 R

123 5 VF 450 17 R

130 6 VF 500 18 R

150 7 VF 551 19 VF

222 8.5 VF 600 20 R

222 8.5 VF 650 21 VF

250 10 VF 700 22 VF

300 11 R 850 23 VF

333 12.5 R


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Step 5: Solving for U, u, uU = n1*n2+ n1 (n1+1)/2 w1

=81

u= (n1*n2)/2= (11*12)/2= 66

u= [ n1*n2(n1+n2+1)/12]= 16.24

Step6 : : Observed z value is:z= (U- u)/ u= (81-66)/16.24= .9236

Step 7 : p value associated is 0.3212.FINAL P VALUE = 0.5-0.3212

=0.17880.1788>0.05, hence the null hypothesis is accepted. Step8 :the monthly expenditure of both the groups is not equal, hence we neefind out the shortcomings in the companys policies, procedure, tarrif voucheoffered, talk time provided. Because people are spending less on our companwill thereby reduce the customer base of company, so we need to keep in pacwith the offers iven b our com etitors as well

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