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The document presents a statistical analysis using a chi-square test to determine the relationship between smoking and cancer. The null hypothesis states that cancer is dependent on smoking, while the alternate hypothesis suggests otherwise. The analysis concludes that the chi-square value of 58.2 is significantly greater than the critical value of 3.841, leading to the rejection of the null hypothesis and indicating that cancer is not dependent on smoking.

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24 views3 pages

Text

The document presents a statistical analysis using a chi-square test to determine the relationship between smoking and cancer. The null hypothesis states that cancer is dependent on smoking, while the alternate hypothesis suggests otherwise. The analysis concludes that the chi-square value of 58.2 is significantly greater than the critical value of 3.841, leading to the rejection of the null hypothesis and indicating that cancer is not dependent on smoking.

Uploaded by

theshalomjessica
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Name:

Adiazi favour chidima


Matric number:
230902517
Course code:
MAS 222
Course Title:
Introduction to statistics for mass communication II
Lecturer:
Dr Balouga
Instructions:
Give yourself a befitting problem in the test of hypothesis and
solve it. It should be 2 pages long.
The submission date is *Monday*, next week.
Submission time is *1 pm*.

Adiazi favour chidima - 230902517


Analyze the below data and tell whether you can conclude that smoking
causes cancer or not

Category Diagnosed as Without Total


cancer cancer
Smoker 400 300 700
Non smoker 300 500 800
Total 700 800 1500

Chi square test check the independence of the two categorical variable.
Here in this question we need to test whether smoking and cancer are
independent or dependent to each other. Hence will perform chi square
test.
Solution:

Step 1:
H0 (Null Hypothesis): Cancer is dependent on smoking
H1 (Alternate Hypothesis): cancer is not dependent on smoking

Step 2:
Calculate the expected value for each cell of the table (when null
hypothesis is true)

The expected values specify what the values of each cell of the table would
Be if there is no association between the two variables.
The formula for computing the expected values requires the sample
size, the
Row totals, and the column totals.
Expected value (e) = (row total * column total)/table total
Now lets create another table with observed and expected values both:

Category Diagnosed as Without cancer Total


cancer
Smokers o = 400 o = 300 700
e= e
700×700/1500=326 =700×800/1500=373

Non o = 300 o=500 800


smokers e= e=800×800/1500=426
800×700/1500=373
Total 700 800 1500

Step 3:
Calculate the chi square value:
Χ2 = Σ[(o-e)2]/e
Χ2 = (400-326)2/326 + (300-373)2/373 + (300-373)2/373 + (500-426)2/426
Χ2 = 16.79 + 14.28 + 14.28 + 12.85
Χ2 = 58.2

Adiazi favour chidima -230902517


Step 4:
Decide if χ2 is statistically significant.

The final step of the chi-square test of significance is to determine if the


value
Of the chi-square test statistic is large enough to reject the null hypothesis.
Now will check χ2 table for the critical value with α = 5%
So from table we got χ2 (critical value at α = 5%) = 3.841
The chi-square value of 58.2 is much larger than the critical value of 3.84,
so
The null hypothesis can be rejected.
Which means with given data, it can be significantly concluded that cancer
is not dependent on smoking.

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