Are the new quarters fair? Data collection: Use 5 quarters with different backs

Question

Are the new quarters fair?

Data collection: Use 5 quarters with different backs (i.e., different states or National Parks). Flip each one 50 times and count the number of heads for each coin. State which coins you used. Do not use a coin flip simulator.

For each coin, perform a hypothesis test. Which hypothesis test is appropriate? Are the conditions met? State your null and alternative hypotheses. Calculate the test statistics. Using a significance level of a=0.05, decide whether to reject or not reject the null hypothesis. What is your conclusion?

coin#1 CA 2016 29 Heads
coin #2 VA 2015   27 Heads
coin #3 AL 2009    31 Heads
coin#4 NV 2000. 23 Heads
coin #5 OH 1999 28 Heada

Explanation / Answer

Coin # n x pcap=x/n Hypothesis Test Conditions Met H0 H1 SE = sqrt(p*(1-p)/n) Test statistics, z = (pcap - p)/SE p-value Decision 1 50 29 0.58 z-test Yes p = 0.5 p not equals 0.5 0.070710678 1.13137085 0.257899035 Fail to Reject 2 50 27 0.54 z-test Yes p = 0.5 p not equals 0.5 0.070710678 0.565685425 0.571607645 Fail to Reject 3 50 31.00000 0.62 z-test Yes p = 0.5 p not equals 0.5 0.070710678 1.697056275 0.089686022 Fail to Reject 4 50 23 0.46 z-test Yes p = 0.5 p not equals 0.5 0.070710678 -0.565685425 0.571607645 Fail to Reject 5 50 28 0.56 z-test Yes p = 0.5 p not equals 0.5 0.070710678 0.848528137 0.396143909 Fail to Reject

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