Question

Alligators and crocodiles can sometimes be confused with each other, but how do their egg hatch rates compare? Define p1 as the proportion of alligator eggs that hatch and p2 as the proportion of crocodile eggs that hatch. Researchers observed a randomly chosen alligator’s clutch with 45 eggs that had 35 eggs successfully hatch and a random crocodile’s clutch with 40 eggs that had 21 eggs successfully hatch

Part 1: Assume the necessary conditions for inference have been met. Construct a 95% confidence interval for the difference in proportions (p1−p2). Make sure to show all of your work, including the necessary formulas used with plugged in values.

Confidence Interval:

Formula with values plugged in:

Part 2: Interpret the confidence interval from above in the context of the problem by completing the following statement. Make sure to include the direction of your difference in the interpretation to receive credit.“We are 95% confident that ...”

Part 3: The researchers used the same parameter definitions given at the top of the page to test H0:p1−p2= 0 vs. HA:p1−p26= 0. The P-value was 0.014. Which of the following statements about the relationship between alligator and crocodile clutch size is true based on this P-value (circle one)?

(a) We can reasonably conclude that alligators and crocodiles have exactly the same hatch rates and should be confused with each other.

(b) We have overwhelming evidence that the alligator hatch rate is different than the crocodile hatch rate.

(c) We can conclude that alligators and crocodiles have differing hatch rates at theα=.05 level.

(d) We can conclude that the alligator hatch rate is the same as the crocodile hatch rate at theα=.05level.

(e) The sample sizes are too small so we should throw out this study

Answer 1