Question

WG	G
1	M
2	M
7	F
4	M
12	F
2	M
1	M
10	F
1	M
2	M
3	M
1	M
1	M
2	M
1	M

Assume that :

The first column is the weight gain of the people in the quarantine in the first week in kilogram (WG) .

   The second column is describing the gender whether it was male or female (G) .

Q: Is there any statistical evidence that the gaining weight for the females is higher than the gaining weight for the males ? Show your work .  

Answer 1

Assuming the data to follow the Normal distribution, we can proceed as follows :-

Let us define the mean and variance weight gain of males as um and sm with n1 number of samples.

Let us define the mean and variance weight gain of females as uf and sf with n2 number of samples.

Step 1 : Define the Hypothesis.

Ho : There is no significant difference in the mean weight gained by the males and the females .i.e. um = uf

H1 : The mean weight gained by the females is significantly greater than that of males .i.e. um < uf  

Step 2 : Define the Level of Significance :

(l.o.s.) = 0.05 ( assumed this as nothing is mentioned in the question.)

Step 4 : Define the test statistics :

Two-sample t-test (since the population standard deviation is unknown, we make use of Student's t-distribution)

Step 5 : Determine the decision criteria : Reject Ho at 5% l.o.s. if tcal < ttab , where ttab = t , n1+n2 - 2 = t0.05 , 13 = 1.771 and  tcal = d / [ sp *(1/n1 + 1/n2 ) ]

Here d =  um - uf  and sp2 = ( (n1 -1) * s12 + (n2 -1) * s22 ) / (  n1 + n2 - 2 )

Step 6 :- Calculations :

n1 = 12 , n2 = 3 , um = 1.75 , uf = 9.6667 , s12  = 0.93182 ,   s22 = 6.33333 , sp2 = 1.762822 and d = -7.9167

Therefore, tcal = -7.9167 / [1.762822 * ( 1/12 + 1/3 ) ] = -6.95731

Step 7 : Conclusion ; Since, tcal < ttab we reject Ho at 5% l.o.s and thus conclude that the mean weight gained by the females is significantly greater than that of males.