Hill and Barton (Nature, 2005) conducted a study to investigate whether Olympic athletes in certain uniform colors have an advantage over their competitors. They noted that competitors in the combat sports of boxing, Taekwando, Greco-Roman wrestling, and freestyle wrestling are randomly assigned to wear red or blue uniforms. For each match in the 2004 Olympics, they recorded the uniform color of the winner. Hill and Barton found that in the 457 matches, the competitor wearing red won 248 times (54.3%), whereas the person wearing blue won 209 times (45.7%). Construct a 99% confidence interval based on these data using Theory-Based Inference applet.Data from the Centers for Disease Control and Prevention indicate that weights of American adults in 2005 had a mean of 167 pounds and a standard deviation of 35 pounds. Calculate the standard deviation of the sample mean for samples of size 47. i !In order to understand why consumers visit their store, a local business conducts a survey by asking the next 100 people who visit their store to fill out a short survey. The business finds that 40 of the 100 people state that the main reason they visited the store was because the store is running a sale on coats that week. If you took repeated samples of size 100 and constructed a 99% confidence interval for the population proportion who would shop at the store because of the coat sale from each sample, what percentage of these intervals would capture the population proportion? i %Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food are seals and other marine animals, which they hunt from a platform of sea ice. Scientists are concerned that global warming is melting these platforms earlier in the year, reducing the time polar bears are able to hunt and forcing them inland without the necessary fat reserves built up to survive summer and fall. The US Geological Survey (USGS) conducted a study in the Southern Beaufort Sea to investigate whether climate change has appeared to negatively impact the weight of polar bears, on average. Eighty-three adult male polar bears were captured between March and May of the years 1990 and 2006 and their weights were recorded. The sample mean weight was 324.6 kg and the sample standard deviation was 88.3 kg. Use the 2SD method to find a 95% confidence interval for parameter of interest