High School

It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome.

A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

Are the conditions for inference met for conducting a z-test for one proportion?

A. Yes, the random, 10%, and large counts conditions are all met.
B. No, the random condition is not met.
C. No, the 10% condition is not met.
D. No, the large counts condition is not met.

Answer :

Yes, the conditions for inference are met for conducting a z-test for one proportion. The random, 10%, and large counts conditions are all met.

We can proceed with the test to determine if there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The random, 10%, and large counts conditions are all met for conducting a z-test for one proportion in this case. The student flipped the glued pennies stack 100 times, providing a sufficient sample size, and each flip is independent, meeting the random condition. Since the number of flips is less than 10% of all possible flips, the 10% condition is met. Finally, with 46 edge landings and 54 non-edge landings, both values exceed 10, meeting the large counts condition.

Learn more about z-test here

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