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                                                                                                                                 Suppose you want to know the true proportion of satisfied customers from a survey to within a margin of error of no more than 0.025 for a 94% confidence interval. What sample size do you need to use if you have prior information that the true proportion is equal to 0.4? Your answer must be a whole number.

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                                                                                                                                 A recent election poll shows that 251 out of 450 likely voters surveyed in the U.S. House Indiana District 9 support the incumbent Erin Houchin (R). Suppose we are interested in conducting a hypothesis test on whether she will get more than 50% of the vote.  Let . What is the p-value? Round to 4 decimals.

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                                                                                                                                 Following a pollutant leak in a nearby pond, a researcher is concerned that the frogs living near this pond may have become contaminated. If more than 10% of frogs living near the pond have become contaminated, county officials will need to shut down the pond and perform emergency cleaning measures. A county official collects a sample of 100 frogs and finds 8 of these frogs to be contaminated. Are the guidelines met for conducting a hypothesis test for a single proportion?