question 28 the following spreadsheet shows r...
question 28 the following spreadsheet shows results of a commute - time survey at a company for 17 randomly selected employees from the companys total of 1,000 employees. in what approximate range is the average commute time for the 1,000 employees highly likely to fall? i commute time (minutes) average 35.94 standard deviation 9.06 sample size (n) 17 margin of error 4.31 1.96×stddev/√n 35 27 48 35 43 45 49 23 34 24 36 31
Answer
# Explanation:
## Step1: Recall confidence - interval formula
The confidence - interval for the population mean when the population standard deviation is unknown (but we have a sample) is given by $\bar{x}\pm E$, where $\bar{x}$ is the sample mean and $E$ is the margin of error. Here, $\bar{x} = 35.94$ and $E=4.31$.
## Step2: Calculate the lower bound
The lower bound of the confidence - interval is $\bar{x}-E$. So, $35.94 - 4.31=31.63$.
## Step3: Calculate the upper bound
The upper bound of the confidence - interval is $\bar{x}+E$. So, $35.94 + 4.31 = 40.25$.
# Answer:
The average commute time for the 1000 employees is highly likely to fall in the range of 31.63 to 40.25 minutes.