Marine biologists have noticed that the color of the outermo

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 33 clam shells in March. 12 of the shells from February had a dark color on the outermost growth band, whereas 18 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 = 0.1.
Note: Do all calculations as February - March

A) The point estimate for the true difference in proportion of dark growth bands between February and March is:  

   Note: answer using 4 decimal precision

B) The test statistic, z_test, is:  
   Note: answer using 2 decimal precision

C) The p-value is:  
   Note: answer using 4 decimal precision

D) The correct decision is:

Reject Ho and conclude that the proportion of dark colored shells are different in February and March

FTR Ho and do not conclude that the proportion of dark colored shells are different in February and March    

Reject Ha and do not conclude that the proportion of dark colored shells are different in February and March

FTR Ha and conclude that the proportion of dark colored shells are different in February and March

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 =12, n1 =50, P1= X1/n1=0.24
Sample 2 : X2 =18, n2 =33, P2= X2/n2=0.545
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.361
Q^ Value For Proportion= 1-P^=0.639
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.24-0.545)/Sqrt((0.361*0.639(1/50+1/33))
Zo =-2.835
| Zo | =2.835
Critical Value
The Value of |Z | at LOS 0.1% is 1.645
We got |Zo| =2.835 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -2.8348 ) = 0.0046
Hence Value of P0.1 > 0.0046,Here we Reject Ho

[ANSWER]

1. Poinr estimate = P^=0.361
2. Zo =-2.835
3. ( P != -2.8348 ) = 0.0046
4. Reject Ho and conclude that the proportion of dark colored shells are different in February and March