A musicologist is currently writing a report about pop songs in the late 2010s. As a part of her research, the musicologist would like to estimate the mean length of pop songs in the late 2010s. A random sample of 207 pop songs from the 2010s was selected and the average of the sample was found to be 3.16 minutes. Suppose the standard deviation of the lengths of all pop songs in the late 2010s is known to be 0.2 minutes. Find three different confidence intervals one with a 98% confidence level, one with a 96% confidence level, and one with a 90% confidence level - for the average length of all pop songs in the late 2010s. Notice how the confidence level affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Round solutions to three decimal places, if necessary. • The margin of error for a 98% confidence interval is given by E A 98% confidence interval is given by • The margin of error for a 96% confidence interval is given by E = A 96% confidence interval is given by • The margin of error for a 90% confidence interval is given by E A 90% confidence interval is given by If the level of confidence is decreased, leaving all other characteristics constant, the margin of error of the confidence interval will increase If the level of confidence is decreased, leaving all other characteristics constant, the width of the confidence interval will decrease

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