Question: Given the average time to complete IRS Form 1040 is 10.53 hours with a standard deviation of 2 hours, and we're considering a sample of
Given the average time to complete IRS Form 1040 is 10.53 hours with a standard deviation of 2 hours, and we're considering a sample of 36 taxpayers, we can calculate the standard error of the mean to determine if a taxpayer taking more than 12 hours is surprising. The standard error of the mean (SEM) is given by the formula: SEM=n Where: ( \sigma ) is the population standard deviation (2 hours) ( n ) is the sample size (36) Plugging in the values we get: SEM=362=62=0.33 hours Now, to find out how many standard errors away 12 hours is from the mean, we use the formula: Z=SEMX Where: ( X ) is the value we're comparing (12 hours) ( \mu ) is the population mean (10.53 hours) So: Z=0.331210.534.45 A Z-score of 4.45 is quite high, indicating that 12 hours is more than four standard errors above the mean. In a normal distribution, this would fall into a very high percentile, making it an unusual event. Therefore, it would be surprising if a taxpayer finished his or her Form 1040 in more than 12 hours because it is significantly higher than the average time, based on the assumed standard
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