7 points] 7. On Thursday, May 24, President Trump suddenly announced that the U.

Question

7 points] 7. On Thursday, May 24, President Trump suddenly announced that the U.S. would pull out of the peace summit with North Korea scheduled for June 12. When this happened, the White House gift shop suddenly discounted the price for the commemorative coin created for the event, which in turn caused the gift shop website to crash because collectors went wild trying to get the coin. Luckily, your friend got an official coin and has been lipping it ever since. Based on her experience, she thinks the coin is unfair and has a 75% chance of coming up heads. To test this theory, you decide to flip the coin 4 times and record how many heads show up. You then repeat this process for a total of 2500 times, giving the results below Heads count | 0 2 4 How many times 12 119 523 1044 802 Conduct a hypothesis test to determine if your friend's claim is reasonable using a 0.08. You must 1) define varaible(s), 2) write hypotheses, 3) calculate a test statistic by hand (only basic mathematical operations allowed on the calculator), 4) ind bounds on the P-value (or an exact value), 5) draw a conclusion for the test, and 6) list the conditions for inference and comment whether they are met

Explanation / Answer

1. The number of heads appear in 4 coin tossing experiment which is 2500 time tossed
2. H0: The coin is unfair i.e. P = 0.75
H1: The coint is fair i.e. P not - 0.75
3. From the given data

Num Categories: 5
Degrees of freedom: 4

Test Statistic, X^2: 0.7322
4) P-Value: 0.9473

5) Here P-value > alpha 0.08 so we accept H0

6) Thus we conclude that the coin is unfair i.e. P = 0.75

We find the expected frequencies and ?2 goodness of fit by the following table X observed Binomial Expected Approxi (Oi-Ei)^2 ((Oi-Ei)^2)/Ei freq (Oi) probabilities freq (Ei) 0 12 0.0039 9.75 10 4 0.4 1 119 0.0469 117.25 117 4 0.0342 2 523 0.2109 527.25 527 16 0.0304 3 1044 0.4219 1054.75 1055 121 0.1147 4 802 0.3164 791 791 121 0.153 Total 2500 ?2 cal     = 0.7323

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