Differences in Absentees in the Workplace between Smokers and Non-smokers

The unit of observations were random samples of twenty-five various employees divided into two distinct, independent populations, smokers and non-smokers. Then data on their absences from work for the previous year were obtained and used in this statistical inference. Because of a strong association between smoking and ill-health, it is generally accepted that smokers miss more work than their non-smoking counterparts. Does the smoker miss more work than the non-smoker? Data from these random samples were used to draw a conclusion….

SMOKERSDATA **VERSUS**DEFINITION NON-SMOKERSTABLE

Unit of Observation: Smoking and Non-Smoking Employees

Variable Name: Definition: Unit of Measurement: Data Source:

Smoker Employee Days Absent in Past Year http://lad.org/issues/4/horizon.html;

Smokes July 11, 2000

Non-Smoker Employee Does Days Absent in Past Year http://lad.org/issues/4/horizon.html;

NOT Smoke July 11, 2000

RANDOMDATA SAMPLESLISTING

Smokers: Absentees: Non-Smokers: Absentees:

Employee 1 10 Employee 1 5

Employee 2 8 Employee 2 9

Employee 3 18 Employee 3 2

Employee 4 8 Employee 4 10

Employee 5 11 Employee 5 12

Employee 6 17 Employee 6 11

Employee 7 19 Employee 7 6

Employee 8 21 Employee 8 9

Employee 9 16 Employee 9 12

Employee 10 2 Employee 10 8

Employee 11 4 Employee 11 4

Employee 12 12 Employee 12 7

Employee 13 11 Employee 13 13

Employee 14 6 Employee 14 6

Employee 15 9 Employee 15 7

Employee 16 13 Employee 16 11

Employee 17 24 Employee 17 10

Employee 18 15 Employee 18 18

Employee 19 14 Employee 19 20

Employee 20 3 Employee 20 4

Employee 21 0 Employee 21 10

Employee 22 9 Employee 22 2

Employee 23 11 Employee 23 8

Employee 24 19 Employee 24 5

Employee 25 10 Employee 25 10

Mean: 11.6 Mean: 8.76

Standard Deviation: 6.110100927 Standard Deviation: 4.352011029

Variances: 37.33333333 Variances: 18.94

SOURCE: http://lad.org/issues/News/4/horizon.html; July 11, 2000

STATISTICAL ANALYSISOUTPUT

F-Test Two-Sample for Variances

Smokers Non-Smokers

Mean 11.6 8.76

Standard Deviation 6.110100927 4.352011029

Variance 37.33333333 18.94

Observations 25 25

df 24 24

F 1.971136924

P(F<=f) one-tail 0.051571253

F Critical one-tail 1.983757159

t-Test: Two-Sample Assuming Equal Variances

Smokers Non-Smokers

Mean 11.6 8.76

Variance 37.33333333 18.94

Observations 25 25

Pooled Variance 28.13666667

Hypothesized Mean Difference 0

df 48

t Stat 1.892940764

P(T<=t) one-tail 0.032201762

t Critical one-tail 1.677224191

P(T<=t) two-tail 0.064403523

t Critical two-tail 2.01063358

CAN WE ACCEPT THESTATISTICAL NULL HYPOTHESISANALYSIS

The data source used in this inference was found through a search engine, http://www.google.com. After hours of surfing the web and grueling through mounds of data I used two of the random samples found at http://lad.org/issues/News/horizon.html.

For this statistical inference, the question was whether the means were truly different or could they have been samples from the same population. To do draw a conclusion, we must first assume normal distribution. We must also set the null hypothesis to m1 - m2 = 0. And per this assignment we must set the a-level at .05 and the hypothesis alternative to m1 - m2 ¹ 0; thus requiring a two-tailed test.

The random samples have a mean of 11.6 days absent for the smoker and 8.76 days absent for the non-smoker. All of my calculations were done using the data analysis tool in Excel but can be done manually with given equations:

Sample Mean ( ): n = sample size

The variances of each sample are 37.33333333 for the smoking population and 18.94 for the non-smoking population. Their standard deviations are 6.