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sibr4566
sibr4566
03.06.2021 • 
Mathematics

A large school district knows that 75\%75%75, percent of students in previous years rode the bus to school. Administrators wondered if that figure was still accurate, so they took a random sample of n=80n=80n, equals, 80 students and found that \hat p=65\% p ^ ​ =65%p, with, hat, on top, equals, 65, percent of those sampled rode the bus to school. To see how likely a sample like this was to happen by random chance alone, the school district performed a simulation. They simulated 120120120 samples of n=80n=80n, equals, 80 students from a large population where 75\%75%75, percent of the students rode the bus to school. They recorded the proportion of students who rode the bus in each sample. Here are the sample proportions from their 120120120 samples: A dot plot for simulated sample proportions has a scale from 0.60 to 0.90 in increments of 0.025. The distribution is slightly right skewed between 0.6125 and 0.86625, with dots plotted as follows. 0.06125, 1. 0.0625, 2. 0.06375, 1. 0.6625, 6. 0.675, 3. 0.6875, 5. 0.70, 6. 0.7125, 5. 0.725, 5. 0.7375, 10. 0.75, 12. 0.7625,16. 0.775, 10. 0.7875, 10. 0.80, 11. 0.8125, 7. 0.825, 6. 0.8375, 1. 0.85, 1. 0.8625, 2. They want to test H_0: p=75\%H 0 ​ :p=75%H, start subscript, 0, end subscript, colon, p, equals, 75, percent vs. H_\text{a}: p \neq 75\%H a ​ :p  ​ =75%H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 75, percent where ppp is the true proportion of students in this district that ride the bus to school. Based on these simulated results, what is the approximate ppp-value of the test? Note: The sample result was \hat p=65\% p ^ ​ =65%p, with, hat, on top, equals, 65, percent. Choose 1 Choose 1 (Choice A) A p\text{-value}\approx 0.07p-value≈0.07p, start text, negative, v, a, l, u, e, end text, approximately equals, 0, point, 07 (Choice B) B p\text{-value}\approx 0.058p-value≈0.058p, start text, negative, v, a, l, u, e, end text, approximately equals, 0, point, 058 (Choice C) C p\text{-value}\app

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