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1. Based on past data, it is known that about 88.26% of flights are on time. Suppose we take a sample of 500 flights and find that 76.96% of them are on time. We want to see if there is evidence that the percentage of flights that are on-time is decreasing.
a. If I wanted to control my margin of error and set it to 1% with 99% confidence, what sample size would I need to take instead of the 500?
b. Using my original sample size of 500, what would be the 99% confidence interval for the population proportion?
c. What are the null and alternative hypotheses?
d. What is the critical value at 99% confidence?
e. Calculate the test statistic (using the sample of 500).
f. Find the p-value.
g. What conclusion would be made here at the 99% confidence level?
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