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 ?=.05α=.05) that the foreman is rigging the coin tosses.

Answer 1

Answer: In this given problem  we have to use one sample z test for the population proportion. The null and alternative hypotheses for this test are given as below:

Step 1: Firstly find the proportion and then stated the hypothesis

If the foreman is not rigging the coin tosses then the proportion p = 10/12 = 0.834

Null hypothesis: H0: The foreman is not rigging the coin tosses. i.e p = 0.834

Alternative hypothesis: H1: The foreman is not rigging the coin tosses. i.e p < 0.834

Step 2: Now   perform the z test for one proportion

Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a left- tailed test is ze = -1.64. The rejection region for this left-tailed test is R = {z:z < -1.64} Test Statistics The Z-statistic is computed as follows: P - po po (1 - pon 0.8333 - 0.834 == -0.006 0.834(1 -0.834)/12 Decision about the null hypothesis Since it is observed that z = -0.006 > 2c = -1.64, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.4975, and since p=0.4975 > 0.05, it is concluded that the null hypothesis is not rejected.

Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is less than po, at the a = 0.05 significance level.

Since for the conclusion we can say The foreman is not rigging the coin tosses.