Answer the following concept questions in 1-3 sentences each. (a) Is a sample mean likely to be exactly equal to the population mean? Explain why or why not. (b) Will the sample mean (or sample proportion) always be inside a confidence interval for the population mean (or the population proportion)? Explain why or why not. (c) Suppose you have one dataset. You create two different confidence intervals from it, a 92.6% confidence interval, and a 96.2% confidence interval. Which interval will be wider? (d) Setup: You obtain a dataset from a random sample. You double-checked your dataset, and there were no typos, and no errors. . All conditions were met to develop a confidence interval. . You develop a 94% confidence interval for the population proportion p, and your con- fidence interval is 0.465 < p < 0.685. You double-checked your calculations, and everything was done correctly. Question: Later, you find out that the actual population proportion is p = 0.39. Why doesn't your confidence interval contain the actual population proportion? 2/2 4h (e) Explain why you might want to potentially use the formula n instead of n > 2/2P (1 p) h when calculating the sample size required when finding a confidence interval for the population proportion. In the formula, h represents the amount of error you are willing to accept, and represents the sample proportion.