A coin is tossed 100 times, landing heads 61 times. Find exact and approximate 80%, 90%, 95%, and 99% confidence intervals for the true probability that the coin will land head.

To determine the effect, if any, of red light on mosquitoes, 958 mosquitoes were placed in the center of a metal type which had a red light source at one end and a white light source at the other. After 2.5 minutes, 642 mosquitoes were found in the red end of the tube. Set up and test the appropriate hypotheses. Find the exact p-value, and use a normal approximation to approximate the p-value. What assumptions do you have to make about the behavior of the mosquitoes?

There is a theory that the anticipation of a birthday can prolong a person's life. In a study set up to examine that notion statistically, it was found that only 60 of 747 people whose obituaries were published in Salt Lake City in 1975 died in the three-month period preceding their birthday. Test the appropriate hypotheses and state your conclusion. Find both the exact p-value, and an approximation for the p-value using a normal approximation.

A newspaper in a certain state wishes to conduct a survey to estimate the support for a certain candidate in the upcoming gubernatorial election. How many voters do they need to sample to ensure that the margin of error in the resulting confidence interval is no greater than plus or minus three percentage points? Would there be a difference in the sample size if they were sampling in Vermont as opposed to sampling in California?