The super villain Gru has a new shrink ray. He has decided to test it on various objects before pulling off a big job. In an attempt to determine how his shrink ray performs, attempts to shrink 200 random objects found in his laboratory. Of the 200 objects he attempts to shrink, 175 of them shrink successfully.

Gru's competition, super villain Vector, has also been testing a shrink ray. He tested his shrink ray on 250 random objects in his laboratory, and 229 of them were shrunk successfully. One of Gru's minions, serving as a spy, reports this information to Gru. Help Gru determine if there is evidence, at a 5% significance level, that there is a difference in proportion of objects successfully shrunk between the two shrink rays. Perform the full procedure.

a) Write out the null and alternate hypothesis. Define any symbols that you use.

b) Verify the assumptions and conditions necessary for inference.

c) Report the following:

Standardized Test Statistic :

 p-value:

d) Write a conclusion in context.