An Analyst wants to know if there was a significant difference in the average of hours worked in a week from 2000 (Group 1) to 2004 (Group 2). He gathers all the data from the General Social Survey, and lists the following summary statistics from the sampling.

Year 2000 2004
Mean 27.34 48.12
Std. Dev 10.11 19.23
Unweighted n 43 54

Required:
What is the correct null hypothesis?

Answer:

H0 : μ2004 - μ2000 = 0

Step-by-step explanation:

Given the data:

Year ________: 2000 ___ 2004

Mean ________ 27.34 ___ 48.12

Std. Dev _______10.11 ____ 19.23

Unweighted n 43 54

The hypothesis is to test if there was a significant difference in the average number of hours worked in a week from 2000 to 2004 ;

Hence, the null hypothesis will negate the hypothesis, that is there is no difference in the average hours worked in a week from 2000 to 2004

Null hypothesis ; H0 : μ2 - μ1 = 0

Alternative hypothesis ; H1 : μ2 - μ1 ≠ 0

Null hypothesis suggest that there is no significant relationship exist in the given set of single observed variable.. As the null hypothesis negate the hypothesis. Hence the difference is zero and hypothesis for the given problem is,

[tex]H_0; (\mu_1-\mu_2)=0[/tex]

[tex]H_a; (\mu_1-\mu_2)\neq 0[/tex]

For year                     2000         2004

Mean                          27.34          48.12

Standard Deviation   10.11          19.23

Unweighted n             43              54

Null hypothesis suggest that there is no significant relationship exist in the given set of single observed variable.

Now the Analyst want to know if there was a significant difference in the average of hours worked in a week from year 2000 to 2004.

To detect a difference (if there it is) between the average of hours worked in a week from 2000 to 2000, it should be test the null hypothesis that there is no difference between the means against the alternative hypothesis. Therefore,

[tex]H_0; (\mu_1-\mu_2)=D_0=0[/tex]

Versus

[tex]H_a; (\mu_1-\mu_2)\neq 0[/tex]

As the null hypothesis negate the hypothesis. Hence the difference is zero and hypothesis for the given problem is,

[tex]H_0; (\mu_1-\mu_2)=0[/tex]

[tex]H_a; (\mu_1-\mu_2)\neq 0[/tex]

learn more about the null hypothesis here;

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