Business Statistics Report: Analysis of Marriage Premium Hypothesis

This report analyzes the 'marriage premium' in the labor market using data from basketball players. The analysis, based on a hypothesis provided by a chief economist, examines the relationship between marital status and various factors including wages, performance ratings, and productivity. The report utilizes statistical methods like one-sample and two-sample t-tests to evaluate the economist's claims. The findings indicate that married men earn higher wages (more than 10%) and have higher performance ratings compared to single men. However, the analysis reveals that the productivity between married and single men is equivalent. The analysis also establishes that a significant proportion of married male players exhibit high productivity. The report concludes that there is a 'marriage premium' in the labor market, as hypothesized by the chief economist, with specific insights into wages, performance, and productivity.

Running head: BUSINESS STATISTICS
Business Statistics
Name of the Student
Name of the University
Author’s Note

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Executive Summary
The report provides analysis of the hypothesis of the chief economist. The outcomes of the
analysis are:
The wages of married men are higher than single men by more than 10%.
The performance ratings of married men is higher than single men.
The productivity of married and single men are equivalent.
70% of married male players have a higher productivity.
Thus, it can be established that there is a marriage premium in the labour market.

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Table of Contents
Introduction......................................................................................................................................3
Analysis of Data..............................................................................................................................3
Analysis 1....................................................................................................................................3
Analysis 2....................................................................................................................................4
Analysis 3....................................................................................................................................4
Analysis 4....................................................................................................................................5
Conclusion.......................................................................................................................................6

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Introduction
The aim of this report is to analyse the data of basketball players. The data has been
provided by EqRA senior consultant Rachel Ng. The purpose of the analysis is to analyse the
“marriage premium” in the labour market. The information regarding the wages, productivity
and marital status have been provided. The data is to be analysed on the basis of the hypothesis
as provided by the chief economist.
Analysis of Data
Analysis 1
In order to analyse the hypothesis as postulated by the chief economist, the first step is to
get the average wages of single players
The average wage of the single players = 1279.89
Thus an increase of 10% on the wage = 1407.88
To check if the hypothesis as postulated by the chief economist is true a hypothesis test of
one-sample t-test is conducted (Sharpe, DeVeaux and Velleman, 2012, p.369).
The average wage of the players is considered to be normally distributed
To test the Hypothesis:
H0 :The average wage of married players is more than∨equal¿ 1407.88
H0 : μ≥ 1407.88
H1 :The average wage of married players is less than1407.88
H1 : μ< 1407.88
The number of married players = 58
The hypothesis test is done at
 = 0.05 level of significance
Thus the rejection region = z < zα=0.05
The p-value = 0.169
Since the p-value is more than the -level, hence the null hypothesis is not rejected.
Hence the hypothesis of the Chief economist “Married men earn roughly 10% higher
wages than their single counterpart” is found to be true.
Statistics Value
Count 58
Mean 1543.34
Std Dev 1067.20
Std Error 140.13
Hypothesized Mean 1407.88
a 0.05
tails 1
df 57
t stat 0.967
p-value 0.169
t Crit 0.063
Sig no

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Analysis 2
In order to test the second hypothesis of the chief economist, the performance ratings of
single and married men are calculated. The performance ratings are equated with the productivity
of the men.
To check if the hypothesis as postulated by the chief economist is true a hypothesis test of
one-sample t-test is conducted (Sharpe, DeVeaux and Velleman, 2012, p.369).
The average productivity of single players = 17.06
The productivity of the players is considered to be normally distributed.
To test the Hypothesis:
H0 :The productivity of married players is more than∨equal ¿ 17.06
H0 : μ≥ 17.06
H1 :The productivity of married players isless than 17.06
H1 : μ< 17.06
The number of married players = 58
The hypothesis test is done at
 = 0.05 level of significance
Thus the rejection region = z < zα=0.05
The p-value = 0.709
Since the p-value is more than the -level, hence the null hypothesis is not rejected.
Hence the hypothesis of the Chief economist “Married men receive higher performance
ratings than single men; as a result they are more likely to be promoted” is found to be true.
Statistics Value
Count 58
Mean 17.52
Std Dev 9.36
Std Error 1.23
Hypothesized Mean 17.06
a 0.05
tails 2
df 57
t stat 0.376
p-value 0.709
t Crit 0.063
Sig no
Analysis 3
To test the third hypothesis the proportion of married men having productivity more than
the 95th percentile is used.
The productivity of the basketball players is the sum total of their points, rebounds and
assits.
The 95th percentile of the productivity = 4.
The number of married men having productivity more than 4 = 53
The number of married men = 58

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Thus the proportion of married men having productivity more than 4 = 53
58 =0.91
To confirm the hypothesis test for proportions is used (Sharpe, DeVeaux and Velleman,
2012, p.364).
To test the Hypothesis:
H0 :The proportion of menhaving productivity more than 4=70 %
H0 :π =70 %
H1 :The proportion of menhaving productivity less than 4<70 %
H1 : π <70 %
The hypothesis test is done at
 = 0.05 level of significance
The p-value = 0.00
Since the p-value is less than the -level, hence the null hypothesis is rejected.
Hence the hypothesis of the Chief economist “70% of male workers in the 95th percentile of the
productivity distribution are married” is not found to be true.
Analysis 4
In order to test the fourth hypothesis, the productivity of single and married men are
compared.
The average productivity of single men = 17.06
The number of single men in the sample data = 72
The average productivity of married men = 17.52
The number of married men in the sample data = 58
To confirm the hypothesis two-sample t-test assuming unequal variances test is used
(Sharpe, DeVeaux and Velleman, 2012, p.404).
To test the Hypothesis:
H0 :The average productivity of single∧married players are equal
H0 : μsingle =μmarried
H1 :The average productivity of single∧married players are not equal
H1 : μsingle ≠ μmarried
The hypothesis test is done at
 = 0.05 level of significance
Thus the rejection region = z < zα=0.05
The p-value = 0.772
Since the p-value is more than the -level, hence the null hypothesis is not rejected.
Hence the hypothesis of the Chief economist “there exists no basis to this observed
discrimination once productivity is taken into account” is found to be true.

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t-Test: Two-Sample Assuming Unequal Variances
Productivity-UnMarried Productivity-Married
Mean 17.06 17.52
Variance 72.42 87.66
Observations 72 58
Hypothesized Mean Difference 0
df 117
t Stat -0.291
P(T<=t) one-tail 0.386
t Critical one-tail 1.658
P(T<=t) two-tail 0.772
t Critical two-tail 1.980
Conclusion
The data of baseball players has been analysed for various hypothesis as put forward by
the chief economist.
From the analysis of the data it is found that the wages of married men are higher than
single men. In fact the wages of married men are higher by more than 10% than single men.
It is also established that the performance ratings of married men is better than single
men. The performance ratings of the players were assumed to be the summation of their points,
rebounds and assists in the matches they have played. Hence the chances of married men being
promoted are higher.
The analysis also shows that the productivity of both married and single men are equal.
Thus there is no discrimination in the productivity of the players.
The analysis however establishes that the more than 70% of the married male players
have a very high productivity.

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References
Sharpe, N.R., DeVeaux, R.D. and Velleman P.F., 2012, Business Statistics, 2nd Ed, Pearson
Education