Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B = the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky’s proportion of poses held for over a minute is greater than Carla’s?Find the z-table here.
The difference in sample proportions, B − C, has mean 0.29 − 0.35 = −0.06 and standard error √[(0.29 × 0.71)/50 + (0.35 × 0.65)/50] ≈ 0.093. Becky’s proportion is greater when B − C > 0, which corresponds to z = [0 − (−0.06)]/0.093 ≈ 0.64. The area to the right of z = 0.64 is about 0.259, so the probability is 0.259.
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