Are the new quarters fair? Flip 5 different coins 50x times. Data : coin#1 CA 20

Question

Are the new quarters fair? Flip 5 different coins 50x times.

Data :
coin#1 CA 2016 29 Heads 21 Tails
coin #2 VA 2015 27 Heads 23 Tails
coin #3 AL 2009 31 Heads 19 Tails
coin#4 NV 2000. 23 Heads 27 Tails
coin #5 OH 1999 28 heads 22 Tails

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 and state number.

Using a significance level of a=0.05, decide whether to reject or not reject the null hypothesis.

What is your conclusion?

Explanation / Answer

The hypothesis test of the probability of getting heads is equal to 0.5 or not is appropriate since the probability of getting heads/tails = 0.5 implies that the coins are fair.

Null hypothesis -> H0 : p = 0.5

Alternative hypothesis -> H1 : p 0.5

COIN 1 :

> prop.test(29,50)

        1-sample proportions test with continuity correction

data: 29 out of 50, null probability 0.5

X-squared = 0.98, df = 1, p-value = 0.3222

alternative hypothesis: true p is not equal to 0.5

95 percent confidence interval:

0.4326718 0.7151090

sample estimates:

   p

0.58

Since p-value < 0.05, we reject H0 and conclude that the coin is significantly not fair.

COIN 2 :

> prop.test(27,50)

        1-sample proportions test with continuity correction

data: 27 out of 50, null probability 0.5

X-squared = 0.18, df = 1, p-value = 0.6714

alternative hypothesis: true p is not equal to 0.5

95 percent confidence interval:

0.3945281 0.6793659

sample estimates:

   p

0.54

Since p-value > 0.05, we accept H0 and conclude that the coin is significantly fair.

COIN 3:

> prop.test(31,50)

        1-sample proportions test with continuity correction

data: 31 out of 50, null probability 0.5

X-squared = 2.42, df = 1, p-value = 0.1198

alternative hypothesis: true p is not equal to 0.5

95 percent confidence interval:

0.4716328 0.7500196

sample estimates:

   p

0.62

Since p-value < 0.05, we reject H0 and conclude that the coin is significantly not fair.

COIN 4:

> prop.test(23,50)

        1-sample proportions test with continuity correction

data: 23 out of 50, null probability 0.5

X-squared = 0.18, df = 1, p-value = 0.6714

alternative hypothesis: true p is not equal to 0.5

95 percent confidence interval:

0.3206341 0.6054719

sample estimates:

   p

0.46

Since p-value > 0.05, we accept H0 and conclude that the coin is significantly fair.

COIN 5:

> prop.test(28,50)

        1-sample proportions test with continuity correction

data: 28 out of 50, null probability 0.5

X-squared = 0.5, df = 1, p-value = 0.4795

alternative hypothesis: true p is not equal to 0.5

95 percent confidence interval:

0.4134993 0.6973395

sample estimates:

   p

0.56

Since p-value < 0.05, we reject H0 and conclude that the coin is significantly not fair.

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