Question

Leela is trying to decide if a coin is fair. She flips it 100 times and gets 63 heads. Please explain why it might NOT make sense to view 63 heads as enough evidence to conclude the coin is unfair.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.04828
z = (p - P) / S.D

z = 2.693

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 2.693.

Thus, the P-value = 0.004.

Interpret results. Since the P-value (0.004) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that  the coin is unfair.