Question

Every morning the foreman flips a coin to decide which group of planters get first choice of the day's planting sites. You think the foreman doesn't like your group (we won't go into the reasons why, but your suspicions are well-founded) and that he's rigging the coin tosses against your group. You keep track for 12 days and note that 10 of the 12 coin tosses have gone against your group. Test the hypothesis (at α=.05) that the foreman is rigging the coin tosses.

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: The foreman is not rigging the coin tosses.

Alternative hypothesis: Ha: The foreman is rigging the coin tosses.

H0: p = 0.5 versus Ha: p > 0.5

This is an upper or right 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 = 10

n = sample size = 12

p̂ = x/n = 10/12 = 0.833333333

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.833333333 – 0.5)/sqrt(0.5*0.5/12)

Z = 2.3094

Test statistic = 2.3094

P-value = 0.0105

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the foreman is rigging the coin tosses.