Do the data provide sufficient evidence to conclude that the

Do the data provide sufficient evidence to conclude that the mean daily protein intake of 51 female vegetarians and 53 female omnivores differ at the 1% significance level , s1 = 18.82122, s2 = 18.96844, x1 = 39.0392, x2 = 49.9245

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate, mean daily protein intake is differ in both - H1: u1 != u2
Test Statistic
X(Mean)=39.0392
Standard Deviation(s.d1)=18.82122 ; Number(n1)=51
Y(Mean)=49.9245
Standard Deviation(s.d2)=18.96844; Number(n2)=53
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =39.0392-49.9245/Sqrt((354.23832/51)+(359.80172/53))
to =-2.94
| to | =2.94
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 50 d.f is 2.678
We got |to| = 2.9372 & | t | = 2.678
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -2.9372 ) = 0.005
Hence Value of P0.01 > 0.005,Here we Reject Ho

We have sufficient evidence to conclude that the mean daily protein intake differ at
the 1% significance level