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In: Statistics and Probability

Question 1. [7 marks total] Parental leave is often compensated to some degree, but the amount...

Question 1. [7 marks total] Parental leave is often compensated to some degree, but the amount of compensation varies greatly. You read a research article that stated, "across people of all incomes, 47% of leave-takers received full pay during their leave, 16% received partial pay, and 37% received no pay." After reading this, you wonder what the distribution of parental leave payment pay is for low income households. Suppose you conduct a survey of leave-takers within households earning less than $30,000 per year. You surveyed 225 people (selected in a random sample) and found that 51 received full pay, 33 received partial pay, and 141 received no pay.

1.c) [2 marks] Compute the chi-square statistic and comment on the cell (i.e. term in summation) that contributes the most to the statistic.

Solutions

Expert Solution

Null hypothesis :Ho :Distribution of parental leave payment pay matches with the given distribution,

Alternate hypothesis :Ha Distribution of parental leave payment pay does not match with  the given distribution,

Chi-square test for Goodness of fit is appropriate to test this.

Given,

Observed counts
Full pay 51
Partial Pay 33
No pay 141
Total 225

Distribution of parental leave payment pay:

% leave-takers received full pay during their leave : 47%

%  received partial pay : 16%

% received no pay : 37%

Expected counts :

Expected Number of people - full pay = 47% of 225 = (225x47)/100 = 105.75

Expected Number of people - Partial pay = 16 % of 225 = (225x16)/100 = 36

Expected Number people - No pay = 37% of 225 = (225x37)/100 = 83.25

Observed counts Expected Counts
Full pay 51 105.75
Partial Pay 33 36
No pay 141 83.25
Total 225 225

Test Statistic :

Observed counts Expected Counts O-E (O-E)2 (O-E)2/E
Full pay 51 105.75 -54.75 2997.5625 28.3457
Partial Pay 33 36 -3 9 0.25
No pay 141 83.25 57.75 3335.0625 40.0608
Total 225 225 68.6566

Chi-square statistic = 68.6566

The cell that contributes maximum is 40.0608 under the category : No pay;

Observed frequency for no pay is : 141; where as if the 37% is applied, the expected proportion is 83.25;


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