Your PI claims that the proportion of Morpho butterflies in a population that are blue is 0.3 .A sample is independently obtained from this population. Of 200 sampled Morphos, 50 turn out to be blue. Given only this information, carry out a hypothesis test to evaluate the claim. What is closest to the p-value that you obtain?

Complete Question

Your PI claims that the proportion of Morpho butterflies in a population that are blue is 0.3 .A sample is independently obtained from this population. Of 200 sampled Morphos, 50 turn out to be blue.Given only this information, carry out a hypothesis test to evaluate the claim. What is closest to the p-value that you obtain?

A 0.019

B 0.038

C 0.070

D 0.139

The correct answer is  D

Step-by-step explanation:

From the question we are told that  

    The population proportion of blue butterflies is  

    The  sample  size is  

     The  sample mean is  

The  Null Hypothesis is mathematically represented as

The  Alternative  Hypothesis is mathematically represented as

Now the sample proportion is mathematically represented as

substituting values

Generally the test statistics is mathematically represented as

substituting values            

The  p-value for a two-tailed test  is  mathematically represented as

for lower -tail test

 for higher-tail test

for this test i assumed a 0.05 level of significance

Now  

  is the cumulative distribution function for test statistics under the null hypothesis

Which can be calculated using MInitab (A statistics calculator )

  for lower-tail test

     The p-value is not significant

 for higher-tail test

p-value is

sorry not sure

step-by-step explanation: