Fill in the two-way table based on the information below, compute the appropriat
ID: 3243255 • Letter: F
Question
Fill in the two-way table based on the information below, compute the appropriate test statistic value, degrees of freedom, p-value, and make a conclusion!
A large study selects 27000 humans to see if they lied or not and report their gender.
25% of samples are males who lied, and 33% are males who never lied.
27% of samples are females who lied and 15% are females who never lied
Please type whole numbers (integers in the table below):
Based on the above table, compute the appropriate test statistic (correct to 2 decimal places).
Hint: Types of test statistic are z-stat, t-stat, Chi-sq_stat, F_stat, etc. So first decide on the appropriate test and then find the value of the test statistics.
The test statistic value is:
Based on the above test statistic value, the p-value (correct to two decimal places) is:
Lied Male Female Total Yes - Observed Yes - Expected No - Observed No-Expected Total 27000Explanation / Answer
Solution
To fill-in the table, we simply multiply 27000 by the respective percentages given.
Lied
Male
Female
Total
Yes - Observed
6750
7290
14040
Yes - Expected
No - Observed
8910
4050
12960
No-Expected
Total
15660
11340
27000
This is an example of Contingency Chi-square Test for Independence.
Hypotheses:
Null Hypothesis: H0: The two attributes (namely telling/not-telling lies and gender) are independent. Vs Alternative: HA: H0 is false.
Test Statistic
2 = [i = 1.2; j = 1, 2]{(Oij – Eij)2/Eij}, where Oij and Eij are respectively the observed and expected frequencies of the ijth cell in the table.
Under H0, Eij = (ith row total x jth column total)/Grand Total
Calculations:
Eij
Lied
Male
Female
Total
Yes - Expected
8143.2
5896.8
14040
No-Expected
7516.8
5443.2
12960
Total
15660
11340
27000
[Check: row totals and column totals of Eij must be equal to the corresponding row totals and column totals of Oij]
{(Oij – Eij)2/Eij} are given in the table below:
Lied
Male
Female
Total
Yes
238.35915
329.1626374
567.5217886
No
258.22241
356.5928571
614.8152709
Total
496.58156
685.7554945
1182.337059
Distribution and p-value
Under H0, test statistics, 2 ~ 2 distribution with degrees of freedom = 1[(number of rows - 1) x (Number of columns)]
So, p-value = P(21 > 1182.34) = 4.2008E-259
Decision:
Since p-value is very small, much less than even 0.1%, H0 rejected/
Conclusion:
There is sufficient statistical evidence to suggest that whether a person tells lie or not is dependent on the gender of the person.
DONE
Lied
Male
Female
Total
Yes - Observed
6750
7290
14040
Yes - Expected
No - Observed
8910
4050
12960
No-Expected
Total
15660
11340
27000
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