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In: Math

At a local business school, it is typical for some fraction of students to pass an...

At a local business school, it is typical for some fraction of students to pass an Accounting certification exam. Recently, funding was used to develop a new program that was designed to increase the proportion of students who pass the exam. The school that developed this program studied 475 students and found that the percentage of students who passed the certification increased to 72% with a 95% confidence interval of [.68, .76]. The hypothesis test, H0: No improvement / same rate as always vs. H1: The intervention changed the passing rate, was rejected with a p-value of .046.  

  1. Explain what the​ p-value means in this context.

    1. Someone says that they thought that the original pass rate was 67%. If that were true, what would you tell them about the efficacy of the program? Phrase the conclusion properly.

    2. If the alternative hypothesis had been, H1: The intervention increased the passing rate, would the p-value change? If so, how? Would you more or less strongly recommend adoption of the new program?   

    3. Even though this program has been shown to be better​ in that it is “statistically significant”, are there reasons that the school should not adopt it?

    4. What is the relationship between the p-value and the confidence interval?   

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