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

****Use 1 Prop Z test on this

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 numner of test if (t or z) .

What is the P value?

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

What is your conclusion for overall.

Explanation / Answer

SOLUTION :-

Here we have given five different coins each flip 50 times.

We have to test five different hypothesis.

For each coin we have to test the hypothesis that,

H0 : p = 0.5 Vs H1 : p not= 0.5

where p is population proportion.

Now for one sample proportion test the test statistic follows Z-distribution.

Test statistic is,

Z = (p^ - p) / sqrt [p*(1-p) / n ]

where p^ is sample proportion.

n is sample size = 50

p^ = x/n

where x is number of successes or heads.

Assume alpha = level of significance = 0.05

We can test this hypothesis in TI_83 calculator.

steps :

STAT --> TESTS --> 5:1-PropZTest --> ENTER --> Input all the values --> Alternative : select "not= P0" --> ENTER --> Calculate --> ENTER

By using these steps we can test the hypothesis.

coin#1 CA 2016 29 Heads 21 Tails

Here x = 29 and n = 50

Test statistic = 1.13

P-value = 0.2579

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : The population proportion may be 0.5.

coin #2 VA 2015 27 Heads 23 Tails.

Here x = 27 and n = 50

Test statistic = 0.56

P-value = 0.5716

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : The population proportion may be 0.5.

coin #3 AL 2009 31 Heads 19 Tails

Here x = 31 and n = 50

Test statistic = 1.70

P-value = 0.0897

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : The population proportion may be 0.5.

coin#4 NV 2000. 23 Heads 27 Tails

Here x = 23 and n = 50

Test statistic = -0.56

P-value = 0.5716

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : The population proportion may be 0.5.

coin #5 OH 1999 28 heads 22 Tails

Here x = 28 and n = 50

Test statistic = 0.85

P-value = 0.3961

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : The population proportion may be 0.5.

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