# BEA674 Data and Business Decision Making Assignment Sample

## Abstract

This is the study in which secondary data is provided including demographic data and data regarding smoking habits. Data consist of 807 observations and 10 variables. The three categorical variables, age group, gender and smoking status while one quantitative variable, number of cigarettes smoked per day (cigs) were analysed. Chi square test was conducted for hypothesis testing for finding association between age group and smoking status & gender and smoking status. t-test was conducted to find the difference between the average number of cigarettes smoked per day between male and female.

### Introduction

This BEA674 data and business decision making assignment sample aimed at finding any difference observed in the smoking status (smoker or not) in different age groups and gender. This study also tried to find the difference between male and female regarding the average number of cigarettes smoked per day.

### Method

This study contains secondary data consisting of 807 observations and 10 variables. The variable Obs No. is an identifying variable. The variables educ, cigpric, age, income and cigarettes are quantitative variables while gender, age groups, restaurn and smoker are qualitative variables.

Calculations were performed in excel. variable age group, gender and smoker are categorical so chi-square method at two sided 5% level of significance was used to test the hypothesis. Cigs variable is discrete quantitative variable and gender is the grouping variable so two sided independent sample t-test at 5% level of significance was carried out to test the hypothesis.

Chi-square test was carried out in excel by inputting formula and doing manual calculations then table was referred to obtain the tabulated Chi square value. t-test was carried out using Data Analysis toolpak of Excel.

Contingency tables (Observed and expected) for age group and smoker & gender and age group were constructed annually in excel. Data of average number of cigarettes being used by male and female is already grouped and provided.

Chi Square was calculated using following formula –

where O = observed value  and E = expected value

Hypotheses are –
1) age group and smoker
Ho: There is an association between smoking status and age group
H1: There is no association between smoking status and age group

2) gender and smoker
Ho: There is an association between gender and age group
H1: There is no association between gender and age group

3) Average no. of cigarettes between male and female
Ho: There is no difference between average no. of cigarettes smoked per day between male and female
H1: There is no difference between average no. of cigarettes smoked per day between male and female

#### Result

For the first hypothesis of finding association between age group and smoking status observed and expected frequencies are calculated as below –
Table 1: Observed frequency of smoking status for different age groups -

 Observed Frequency Table Yes No Total Under 19 11 26 37 19-24 44 68 112 25-34 90 112 202 35-44 53 81 134 45-54 60 72 132 55+ 52 138 190 Total 310 497 807

Table 2: Expected frequency of smoking status for different age groups -

 Expected Frequency Table Yes No Total Under 19 14.21 22.79 37 19-24 43.02 68.98 112 25-34 77.60 124.40 202 35-44 51.47 82.53 134 45-54 50.71 81.29 132 55+ 72.99 117.01 190 Total 310 497 807

Table 3: Chi Square of smoking status for different age groups -

 Chisquare Yes No Under 19 0.73 0.45 19-24 0.02 0.01 25-34 1.98 1.24 35-44 0.05 0.03 45-54 1.70 1.06 55+ 6.03 3.76 Total 17.07

Chi Square (χ2) value of the statistic obtained is 17.07. Tabulated value of Chi Square (χ2) obtained at two sided 0.05 level of significance and 5 degree of freedom (2-1*6-1) = 12.833.

For the second hypothesis of finding association between gender and smoking status observed and expected frequencies are calculated as below –
Table 4: Observed frequency of smoking status for different genders -

 Observed Yes No Total Male 273 436 709 Female 37 61 98 Total 310 497 807

Table 5: Expected frequency of smoking status for different genders -

 Expected Yes No Total Male 272.35 436.65 709 Female 37.65 60.35 98 Total 310 497 807

Table 6: Chi Square of smoking status for different genders -

 Chi Square Yes No Male 0.0015 0.0010 Female 0.0111 0.0069 Total 0.02

Chi Square (χ2) value of the statistic obtained is 0.02. Tabulated value of Chi Square (χ2) obtained at two sided 0.05 level of significance and 1 degree of freedom (2-1*2-1) = 5.02.

For the third hypothesis of finding difference between male and female in the average number of cigarettes smoked per day –
Table 7: Independent sample t-test results -

 t-Test: Two-Sample Assuming Unequal Variances Male Female Mean 8.724965 8.408163 Variance 191.8522 164.0585 Observations 709 98 Hypothesized Mean Difference 0 df 130 t Stat 0.227177 P(T<=t) one-tail 0.410321 t Critical one-tail 1.656659 P(T<=t) two-tail 0.820643 t Critical two-tail 1.97838

p-value obtained for two sample t-test is 0.821. t statistic is 0.2272. Critical value of t test at two sided 0.05 level of significance with 130 degree of freedom is 1.98.

#### Discussion

Considering the results presented above, for age group and smoking status, Chi square calculated value is greater than chi square tabulated value (Table 3) implying that we cannot accept Null Hypothesis. Thus, concluding association between age group and smoking status (smoker or not).

For gender and smoking status, Chi square calculated value is smaller than chi square tabulated value (Table 6) implying that we have to accept Null Hypothesis. Thus, concluding no association between gender and smoking status (smoker or not).

For difference between male and female in average number of cigarettes smoked per day (Table 7), on an Average 8.73 cigarettes smoked per day by males was not significantly greater than on an average 8.41 cigarettes smoked per day by females with t(130, 0.05) = 0.2272, p = 0.8206 (> 0.05 level of significance).

In this study we found an association between age group and smoking status. But we fail to find any association between gender and smoking status which is also supported by the t-test result. This study fail to find any difference between number of cigarettes smoked per day by male or female.

### References

1) Chi Square Table. Available from: http://flylib.com/books/en/3.287.1.235/1/ (accessed on 23 Jan 2015)
2) Chi Square Example Handout.  http://uwf.edu/jgould/Spring%202005/Chi%20Square%20Example%20Handout.pdf (accessed on 23 Jan 2015)

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