Respond to the following to describe a "real world" scenario where a researcher might want to construct a confidence interval to support a conclusion about a population parameter. 1. Provide an overview of the scenario and the variable involved. Include an explanation of why and how constructing the confidence interval adds value. I.e., why might this information be important to know? (4 points) A random survey sample of 25 adults is taken to determine the mean length of time an adult person is able to balance on one foot without falling over . The researcher constructs a confidence interval to find a range that estimates the true value for the population of the statistic. The confidence interval is likely to contain the exact value of the unknown population parameter. The value of a confidence interval is important to determine a range of values to best describe a population. As the sample size increases, the error of sampling decrease and the intervals will become narrower. 2. Identify any assumptions that must be met. (3 points) The confidence interval indicates that you are a certain percentage confident that the mean for the entire population falls within the range of the interval. Due to the random nature of the confidence interval, it is unlikely that any two random samples of the population will yield an identical confidence interval. 3. Describe an overview of the process of constructing the confidence interval along with the steps involved. (3 points) The formula used for a confidence interval is determined by the sample size. Since the random survey sample in this case is less than 30 and is assumed the population is normally distributed. The following t-test confidence interval is applied. Lower Limit=meanz ( a2 )( sd( n ) ) upper limit =mean+ z ( a2 )( sd( n) )