Answered step by step
Verified Expert Solution
Question
1 Approved Answer
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
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started