I need to find the pvalue Marine biologists have noticed tha

I need to find the p-value

Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 50 clam shells in February and 41 clam shells in March. 11 of the shells from February had a dark color on the outermost growth band, whereas 15 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months. Let = 0.01.

Solution

Null , There Is No Significance between them Ho: p1 = p2
Alternate , There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =11, n1 =50, P1= X1/n1=0.22
Sample 2 : X2 =15, n2 =41, P2= X2/n2=0.366
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.286
Q^ Value For Proportion= 1-P^=0.714
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.22-0.366)/Sqrt((0.286*0.714(1/50+1/41))
Zo =-1.532
| Zo | =1.532
Critical Value
The Value of |Z | at LOS 0.01% is 2.576
We got |Zo| =1.532 & | Z | =2.576
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -1.5324 ) = 0.1254
Hence Value of P0.01 < 0.1254,Here We Do not Reject Ho