Question

Question: Calcul UNS UIT Logic: Test the Step 1 What is the research problem? null Step 2 What is the null hypothesis? hypothesis What is the alternative hypothesis? that this Step 3 What are the coin is degrees of unbiased, freedom? that is, that What is the decision rule? heads and Step 4 What is the critical tails are X ? equally What is the value of likely to X? (you will need to appear in calculate this) the long Step 5 What is the decision? (retain or reject the run. null hypothesis at the specified level of significance; note the relationship between the observed and critical X scores) Step 6 What is your interpretation of the decision in relation to the original research problem? Specify the p-value for this test result

Answer 1

Hypothesis Testing

A hypothesis is a statement about the value of the parameter being testing. Null-hypothesis is the basis hypothesis being testing. The hypothesis testing may be one-tailed or two-tailed. The conclusion of hypothesis testing can also be drawn by calculating the confidence interval.

Given information

It is observed that among 50 tosses of a coin, there are 30 heads.

Hypothesis Testing:

The null hypothesis will be that the coin is unbiased whereas the alternate hypothesis will be that the coin is not unbiased which means it is a biased coin. So,

Но : р — 0.5

H: p 0.5

The required value of test-statistic will be calculated as,

p- p ~ N (0, 1) , where p p(1-p) T.S : п п

Therefore,

30 p = 50

p = 0.6

0.60 – 0.50 T.S = 0.50x0.50 50 = 1.4142

So, the value of test statistic is 1.4142.

At, 5% level of significance, the critical value for a two-tailed test using the Z-table is 1.96. Since, the test statistic does not lie in the rejection region; we do not reject the null hypothesis. This means that heads and tails are equally likely to appear in the long-run.

Therefore, the coin is unbiased.

P-value:

Now, the required p-value will be calculated as,

$P - value = 2P\left( {Z > T.S} \right)\\ = 2P\left( {Z > 1.4142} \right)\\ = 2\left( {1 - 0.921} \right)\\ = 2 \times 0.079\\ = 0.158$

So, the p-value of the test is 0.158. Since, the value is greater than the level of significance of the test i.e. 5%, we will not reject the null hypothesis which means that the coin is unbiased.