People Attribute More Importance to Leisure or to Work-Statistics Sample

QUESTION

Choose the appropriate statistical test to answer the question ‘do people attribute more importance to leisure or to work?’ are there any sex differences?

provide explanation why you selected particular test and also solve the same in excel.

Sheet 1

Sex	Leisure	Work
1	8	4
1	10	5
1	8	4
1	7	6
1	7	4
1	8	4
1	7	5
1	10	5
1	10	5
1	7	3
1	5	3
1	8	4
1	7	2
1	9	6
1	7	6
1	9	6
1	5	4
1	5	4
1	4	2
1	4	4
1	9	6
1	5	2
1	5	4
1	7	5
1	4	2
1	5	2
1	8	6
1	8	2
1	5	4
1	5	2
1	8	7
1	7	3
1	7	3
1	8	5
1	8	4
1	4	2
1	8	7
1	4	4
1	7	2
1	7	2
1	4	2
1	5	2
1	6	4
1	6	3
1	6	3
1	9	5
1	6	2
1	6	6
1	6	6
1	9	4
1	6	3
1	8	6
1	7	4
1	6	3
1	7	4
1	7	4
1	6	3
1	8	2
1	6	4
1	7	4
1	9	7
1	7	4
1	8	5
1	9	6
1	6	3
1	6	3
1	7	5
1	6	4
1	2	1
1	2	1
1	7	4
1	8	7
1	7	7
1	7	5
1	8	5
1	7	4
1	9	5
1	7	5
1	7	5
1	7	5
1	5	4
1	6	3
1	5	3
1	8	4
1	3	3
1	5	3
1	6	4
1	6	5
1	6	3
1	5	1
1	6	3
1	6	4
1	3	1
1	5	4
1	7	3
1	5	3
1	7	5
1	6	3
1	5	1
1	7	3
1	8	5
1	6	4
1	6	3
1	8	5
1	6	3
1	6	4
1	4	4
1	6	3
1	5	2
1	5	3
1	5	4
1	8	7
1	4	4
1	7	4
1	5	4
1	5	6
1	4	3
1	9	7
1	5	6
1	5	4
1	6	6
1	4	2
1	4	2
1	4	4
1	4	2
1	4	4
1	4	4
1	4	2
1	4	6
1	8	6
1	6	2
1	8	6
1	4	3
1	3	5
1	4	4
1	4	1
1	4	1
1	10	5
1	6	2
1	6	2
1	6	3
1	10	5
1	4	3
1	4	1
1	3	2
1	9	5
1	6	2
1	3	2
1	6	4
1	3	1
1	3	1
1	3	1
1	3	1
1	3	3
1	3	3
1	9	5
1	3	2
1	6	5
1	3	2
1	9	5
1	3	1
1	3	1
1	9	5
1	3	2
1	6	4
1	10	5
1	6	2
1	7	5
1	6	3
1	10	5
1	6	2
1	3	2
1	7	5
1	4	2
1	5	3
1	7	3
1	8	5
1	8	5
1	6	3
1	8	5
1	6	4
1	8	5
1	6	3
1	7	3
1	8	5
1	7	4
1	5	3
1	9	5
1	5	3
1	9	5
1	7	4
1	8	4
1	7	5
2	5	3
2	5	3
2	10	6
2	8	5
2	7	4
2	8	5
2	8	5
2	8	6
2	10	5
2	8	5
2	10	5
2	9	4
2	5	1
2	4	1
2	7	3
2	9	6
2	2	1
2	5	3
2	9	5
2	10	6
2	5	3
2	7	3
2	5	4
2	9	6
2	9	5
2	9	5
2	9	6
2	7	5
2	9	5
2	9	4
2	6	3
2	5	2
2	9	5
2	3	4
2	7	3
2	7	3
2	7	1
2	5	1
2	3	1
2	3	1
2	7	6
2	7	6
2	5	3
2	4	1
2	7	3
2	4	4
2	7	5
2	4	3
2	5	2
2	10	5
2	9	5
2	10	5
2	6	4
2	10	5
2	4	2
2	9	5
2	9	5
2	5	2
2	6	3
2	6	3
2	6	3
2	9	4
2	5	2
2	7	4
2	9	5
2	6	3
2	9	6
2	6	3
2	5	3
2	7	3
2	9	6
2	6	3
2	4	1
2	6	3
2	7	3
2	6	3
2	4	1
2	5	1
2	8	4
2	8	5
2	5	1
2	8	3
2	6	3
2	5	1
2	8	4
2	8	4
2	6	3
2	5	1
2	5	4
2	7	3
2	9	5
2	9	4
2	7	4
2	7	5
2	7	4
2	5	3
2	7	5
2	3	2
2	9	5
2	5	3
2	7	4
2	7	3
2	7	3
2	7	4
2	8	4
2	8	6
2	6	4
2	6	3
2	4	1
2	4	1
2	4	3
2	4	1
2	4	4
2	3	4
2	4	4
2	8	4
2	4	2
2	8	5
2	5	3
2	4	2
2	4	2
2	7	4
2	8	4
2	5	3
2	5	4
2	5	3
2	5	4
2	8	6
2	5	3
2	7	4
2	7	4
2	4	5
2	6	6
2	2	2
2	2	6
2	3	4
2	3	6
2	4	4
2	6	5
2	7	2
2	5	2
2	7	4
2	4	1
2	8	4
2	3	4
2	6	6
2	6	2
2	3	2
2	6	4
2	3	2
2	3	2
2	6	6
2	6	4
2	3	6
2	6	4
2	6	4
2	6	4
2	3	2
2	3	2
2	6	4
2	6	4
2	6	5
2	4	2
2	6	2
2	7	5
2	10	5
2	7	3
2	6	4
2	7	3
2	6	2
2	6	4
2	6	3
2	8	6
2	8	5
2	6	4
2	3	3
2	5	3
2	5	4
2	4	1
2	3	1
2	6	4
2	3	2
2	3	2
2	6	3
2	3	2
2	5	2
2	6	2
2	5	3
2	4	1
2	4	1
2	4	2
2	4	2
2	5	2
2	4	2
2	8	2
2	8	4
2	3	2
2	8	5
2	8	5
2	5	4
2	8	5
2	4	2

ANSWER

Here, we have a dataset having 3 variables i.e. sex,Leisure and work time.

Our first intention is to find whether people attribute more importance to leisure than work.

Here, we have the sample (whole dataset) where we have paired data i.e. we have data of the same person’s leisure time and work time. But the standard deviation of the population distribution is unknown, so here we will do 2 sample paired t test.

To do this test in excel go to : Data-> Data Analysis -> Paired t test for means

For results of this test refer to Sheet 6

Now, here using excel we get, the value of the test statistic as, 32.77197175

Here, we take level of significance as 0.05, so critical t value= 1.648730226

So, as the test statistic’s value is greater than tvalue so we reject the null hypothesis i.e according to the data yes people attribute more importance to leisure than work.

Now, in sheet 2 , we have divided the data into two parts (i.e. Sex = 1 and 2)

For Sex=1, we do the same paired t test (Check results in sheet 7), test statistic’s value is 23.07655089

Here, we take level of significance as 0.05, so critical t value= 1.652828589

So, as the test statistic’s value is greater than t-value so we reject the null hypothesis i.e according to the data yes people (in category of sex=1) attribute more importance to leisure than work.

For Sex=2, we do the same paired t test (Check results in sheet 8), test statistic’s value is 23.30413857

Here, we take level of significance as 0.05, so critical t value= 1.652469842

So, as the test statistic’s value is greater than t-value so we reject the null hypothesis i.e according to the data yes people (in category of sex=2) attribute more importance to leisure than work.

Hence , there are no differences in the opinion for change in sex.

Sheet 2

Sex	Leisure	Work
1	8	4
1	10	5
1	8	4
1	7	6
1	7	4
1	8	4
1	7	5
1	10	5
1	10	5
1	7	3
1	5	3
1	8	4
1	7	2
1	9	6
1	7	6
1	9	6
1	5	4
1	5	4
1	4	2
1	4	4
1	9	6
1	5	2
1	5	4
1	7	5
1	4	2
1	5	2
1	8	6
1	8	2
1	5	4
1	5	2
1	8	7
1	7	3
1	7	3
1	8	5
1	8	4
1	4	2
1	8	7
1	4	4
1	7	2
1	7	2
1	4	2
1	5	2
1	6	4
1	6	3
1	6	3
1	9	5
1	6	2
1	6	6
1	6	6
1	9	4
1	6	3
1	8	6
1	7	4
1	6	3
1	7	4
1	7	4
1	6	3
1	8	2
1	6	4
1	7	4
1	9	7
1	7	4
1	8	5
1	9	6
1	6	3
1	6	3
1	7	5
1	6	4
1	2	1
1	2	1
1	7	4
1	8	7
1	7	7
1	7	5
1	8	5
1	7	4
1	9	5
1	7	5
1	7	5
1	7	5
1	5	4
1	6	3
1	5	3
1	8	4
1	3	3
1	5	3
1	6	4
1	6	5
1	6	3
1	5	1
1	6	3
1	6	4
1	3	1
1	5	4
1	7	3
1	5	3
1	7	5
1	6	3
1	5	1
1	7	3
1	8	5
1	6	4
1	6	3
1	8	5
1	6	3
1	6	4
1	4	4
1	6	3
1	5	2
1	5	3
1	5	4
1	8	7
1	4	4
1	7	4
1	5	4
1	5	6
1	4	3
1	9	7
1	5	6
1	5	4
1	6	6
1	4	2
1	4	2
1	4	4
1	4	2
1	4	4
1	4	4
1	4	2
1	4	6
1	8	6
1	6	2
1	8	6
1	4	3
1	3	5
1	4	4
1	4	1
1	4	1
1	10	5
1	6	2
1	6	2
1	6	3
1	10	5
1	4	3
1	4	1
1	3	2
1	9	5
1	6	2
1	3	2
1	6	4
1	3	1
1	3	1
1	3	1
1	3	1
1	3	3
1	3	3
1	9	5
1	3	2
1	6	5
1	3	2
1	9	5
1	3	1
1	3	1
1	9	5
1	3	2
1	6	4
1	10	5
1	6	2
1	7	5
1	6	3
1	10	5
1	6	2
1	3	2
1	7	5
1	4	2
1	5	3
1	7	3
1	8	5
1	8	5
1	6	3
1	8	5
1	6	4
1	8	5
1	6	3
1	7	3
1	8	5
1	7	4
1	5	3
1	9	5
1	5	3
1	9	5
1	7	4
1	8	4
1	7	5

Sex	Leisure	Work
2	5	3
2	5	3
2	10	6
2	8	5
2	7	4
2	8	5
2	8	5
2	8	6
2	10	5
2	8	5
2	10	5
2	9	4
2	5	1
2	4	1
2	7	3
2	9	6
2	2	1
2	5	3
2	9	5
2	10	6
2	5	3
2	7	3
2	5	4
2	9	6
2	9	5
2	9	5
2	9	6
2	7	5
2	9	5
2	9	4
2	6	3
2	5	2
2	9	5
2	3	4
2	7	3
2	7	3
2	7	1
2	5	1
2	3	1
2	3	1
2	7	6
2	7	6
2	5	3
2	4	1
2	7	3
2	4	4
2	7	5
2	4	3
2	5	2
2	10	5
2	9	5
2	10	5
2	6	4
2	10	5
2	4	2
2	9	5
2	9	5
2	5	2
2	6	3
2	6	3
2	6	3
2	9	4
2	5	2
2	7	4
2	9	5
2	6	3
2	9	6
2	6	3
2	5	3
2	7	3
2	9	6
2	6	3
2	4	1
2	6	3
2	7	3
2	6	3
2	4	1
2	5	1
2	8	4
2	8	5
2	5	1
2	8	3
2	6	3
2	5	1
2	8	4
2	8	4
2	6	3
2	5	1
2	5	4
2	7	3
2	9	5
2	9	4
2	7	4
2	7	5
2	7	4
2	5	3
2	7	5
2	3	2
2	9	5
2	5	3
2	7	4
2	7	3
2	7	3
2	7	4
2	8	4
2	8	6
2	6	4
2	6	3
2	4	1
2	4	1
2	4	3
2	4	1
2	4	4
2	3	4
2	4	4
2	8	4
2	4	2
2	8	5
2	5	3
2	4	2
2	4	2
2	7	4
2	8	4
2	5	3
2	5	4
2	5	3
2	5	4
2	8	6
2	5	3
2	7	4
2	7	4
2	4	5
2	6	6
2	2	2
2	2	6
2	3	4
2	3	6
2	4	4
2	6	5
2	7	2
2	5	2
2	7	4
2	4	1
2	8	4
2	3	4
2	6	6
2	6	2
2	3	2
2	6	4
2	3	2
2	3	2
2	6	6
2	6	4
2	3	6
2	6	4
2	6	4
2	6	4
2	3	2
2	3	2
2	6	4
2	6	4
2	6	5
2	4	2
2	6	2
2	7	5
2	10	5
2	7	3
2	6	4
2	7	3
2	6	2
2	6	4
2	6	3
2	8	6
2	8	5
2	6	4
2	3	3
2	5	3
2	5	4
2	4	1
2	3	1
2	6	4
2	3	2
2	3	2
2	6	3
2	3	2
2	5	2
2	6	2
2	5	3
2	4	1
2	4	1
2	4	2
2	4	2
2	5	2
2	4	2
2	8	2
2	8	4
2	3	2
2	8	5
2	8	5
2	5	4
2	8	5
2	4	2

Sheet 6

t-Test: Paired Two Sample for Means

	Leisure	Work
Mean	6.10379746835443	3.60506329113924
Variance	3.79884341065347	2.23956820664396
Observations	395	395
Pearson Correlation	0.641470645869468
Hypothesized Mean Difference	0
df	394
t Stat	32.7719717473346
P(T<=t) one-tail	6.88563879812429E-115
t Critical one-tail	1.64873022609634
P(T<=t) two-tail	1.37712775962486E-114
t Critical two-tail	1.96600320134887

Sheet 7

t-Test: Paired Two Sample for Means

	Leisure	Work
Mean	6.15025906735751	3.72538860103627
Variance	3.60751295336787	2.31482081174439
Observations	193	193
Pearson Correlation	0.655985500932505
Hypothesized Mean Difference	0
df	192
t Stat	23.0765508881093
P(T<=t) one-tail	1.43355451748573E-57
t Critical one-tail	1.65282858927009
P(T<=t) two-tail	2.86710903497145E-57
t Critical two-tail	1.97239649131558

Sheet 8

t-Test: Paired Two Sample for Means

	Leisure	Work
Mean	6.05940594059406	3.49009900990099
Variance	3.99645337668095	2.15164277621792
Observations	202	202
Pearson Correlation	0.629643104305918
Hypothesized Mean Difference	0
df	201
t Stat	23.3041385685994
P(T<=t) one-tail	2.452581301171E-59
t Critical one-tail	1.65246984196998
P(T<=t) two-tail	4.905162602342E-59
t Critical two-tail	1.97183650677986

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