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A study of second-year college students asked them to rate their preparedness for college during their freshman year on a scale of 0 - 10. The researchers produced a 95% confidence interval for the average preparedness: (5.8, 7.7). They also performed a hypothesis test H0: μ = 5.6 vs. Ha: μ ≠ 5.6 and found a p-value of 0.03. a) When we say "95% confidence," what does that mean? If we were to repeat this sampling method many times, we would expect that 95% of the samples we produced would produce a sample mean between 5.8 and 7.7. A 95% confidence interval has the property that if we repeatedly selected our random sample in exactly the same way, each time constructing a different 95% confidence interval, then in the long run 95% of those intervals would contain the true mean. The probability that this particular interval contains the true average preparedness of incoming students at this school is approximately 95%. We are 95% confident that the mean for the surveyed students is between 5.8 and 7.7. b) When we say that the p-value is 0.03, what does that mean? If the null hypothesis were true, then the true value of the parameter for the proportion of students who felt prepared entering college is 0.03. If the average college preparedness of freshman students is really 5.6, then we could expect to find sample results at least this extreme with a probability of 0.03. If the true average preparedness among these surveyed students is really 5.6, then 0.03 is the probability that the average preparedness among all freshmen at the university is 5.6. If we were to repeat this procedure for many random samples of this size from this population, the proportion of them that would be this far from 5.6 is roughly 0.03.

A study of second-year college students asked them to rate their preparedness for college during their freshman year on a scale of 0 - 10. The researchers produced a 95% confidence interval for the average preparedness: (5.8, 7.7). They also performed a hypothesis test H0: μ = 5.6 vs. Ha: μ ≠ 5.6 and found a p-value of 0.03.

a) When we say "95% confidence," what does that mean?
If we were to repeat this sampling method many times, we would expect that 95% of the samples we produced would produce a sample mean between 5.8 and 7.7. A 95% confidence interval has the property that if we repeatedly selected our random sample in exactly the same way, each time constructing a different 95% confidence interval, then in the long run 95% of those intervals would contain the true mean. The probability that this particular interval contains the true average preparedness of incoming students at this school is approximately 95%. We are 95% confident that the mean for the surveyed students is between 5.8 and 7.7.

b) When we say that the p-value is 0.03, what does that mean?
If the null hypothesis were true, then the true value of the parameter for the proportion of students who felt prepared entering college is 0.03. If the average college preparedness of freshman students is really 5.6, then we could expect to find sample results at least this extreme with a probability of 0.03. If the true average preparedness among these surveyed students is really 5.6, then 0.03 is the probability that the average preparedness among all freshmen at the university is 5.6. If we were to repeat this procedure for many random samples of this size from this population, the proportion of them that would be this far from 5.6 is roughly 0.03.

a study of second year college students asked them to rate their preparedness for college during their freshman year on a scale of 0 10 the researchers produced a 95 confidence interval for 83943

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