Refer to Example 5 but suppose there are two additional design plans \(\mathrm{B}\) and \(\mathrm{C}\) for making miniature drones. Under B, 10 of 40 drones failed the initial test and under C 15 of 39 failed. Consider the results for all three design plans. Use the 0.05 level of significance to test the null hypothesis of no difference in the three probabilities of failing the test.

Data From Example 5

EXAMPLE 5 Selecting a sample size for estimating a proportion Suppose that we want to estimate the true proportion of defectives in a very large shipment of adobe bricks, and that we want to be at least 95% confident that the error is at most 0.04. How large a sample will we need if (a) we have no idea what the true proportion might be; (b) we know that the true proportion does not exceed 0.12?