Question

Male and female students were asked to report how long they spend getting ready for a date:

Men: 28, 35, 52, 14

Female: 30,82,53,61

Conduct all steps of an independent samples t-test and report the result of your test

Answer 1

Given that,

Male and female students were asked to report how long they spend getting ready for a date.

Men/Male: 28, 35, 52, 14

Female: 30,82,53,61

Here we perfrom a  independent samples t-test at 5% level of significance. [5% level of significance means ]

let, Xi = ith data of men students and Yi = ith data of Feamle students

Population mean for men students. and   Population mean for female students.

Null and Alternative Hypothese:

vs

For this testing our appropriate test statistic is gievn by,

Where, Sample Mean for Men students  ,   Sample Mean of for Female students ,

Number of observation for Men students,   Number of observation for Female students ,

Sample Variance for Men students , Sample Varince for Female students ,

and under

Formula:  

  and [ Given ]

and   

and

Table For Calculation:

28	30	-4.25	-26.5	18.0625	702.25
35	82	2.75	25.5	7.5625	650.25
52	53	19.75	-3.5	390.0625	12.25
14	61	-18.25	4.5	333.0625	20.25
Total=129	Total=226			Total=748.75	Total=1385

Calculation: Putting the value from table and we get,

So value of test statistic is given by,

[ round to four decimal places ]

Rejection Rule:

We reject the null htpothesis at level if,

Here, and

[ from t-distribution probability table we get for DF=6 at level and for two tailed test t value is = 2.447 ]

i.e.

Decision/Result: Accept the null hypothesis at level

Coclusion: From the above result we can conclude that at 5% level of significance Men/Male and Female students are same for getting ready for a date.