Question

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. Calculate the p-value and state the conclusion. Use ? = .05.

Answer 1

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. That is probability of head up or tail up is 0.5

Let , p denotes the true probability of a penny landing heads up when flipped.

Hypothesis :

Two tailed test.

Test statistic :

Where , = Sample proportion = 28/50 = 0.56

p = Hypothesized population proportion = 0.5

n = sample size = 50

P-value :

P-value for this two tailed test is ,

p-value = P( z < -0.8485 ) + P( z > 0.8485 ) = 2*P( z < -0.8485 )

Using Excel ,   =NORMSDIST( Z )

P( z < -0.8485 ) = NORMSDIST( -0.8485 ) = 0.19808

So, P-value = 2*0.19808 = 0.3962

p-value = 0.3962

Decision about null hypothesis :

Rule : Reject null hypothesis if p-value less than significance level

Significance level = 0.05

It is observed that p-value ( 0.3962 ) is greater than = 0.05.

So fail to reject null hypothesis.

Conclusion :

There is sufficient evidence to conclude that pennies are fair, meaning equally likely to land heads up or tails up.