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.

(NO EXCEL)

Answer 1

Solution:

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: Pennies are fair.

Alternative hypothesis: Ha: Pennies are not fair.

H0: p = 0.5 versus Ha: p ≠ 0.5

This is a two tailed test.

We are given

Level of significance = α = 0.05

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 28

n = sample size = 50

p̂ = x/n = 28/50 = 0.56

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.56 – 0.5)/sqrt(0.5*0.5/50)

Z = 0.8485

Test statistic = 0.8485

P-value = 0.3961

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that Pennies are fair.