Groundhog's day is on february 2nd each year. on this day, in punxsatawney, pennsylvania, thousands of onlookers watch to see if phil, the groundhog, will cast a shadow. if he does, then six more weeks of winter are predicted. if he doesn't, then an early spring is predicted. historically, phil's prediction has only been correct about 40% of the time.
using complete sentences, design a simulation to determine the probability that phil's prediction will be correct at least two out of the next three years. make sure to explain how you would use the simulation to determine the probability.

Arandomized controlled trial is designed to evaluate the effect of metoprolol in patients with heart failure. while preparing for statistical analysis, the researcher reviews some common types of statistical errors. which of the following statements is true regarding a type i error in a clinical study? a. the study is not significantly powered to detect a true difference between study groups. bthe null hypothesis is true but is rejected in error. c. the null hypothesis is false but is accepted in error. d. type i error is also known as beta and is usually 0.1 or 0.2. e. type i error depends on the study's confidence interval.