Answer:
The difference between these cut-offs is of $1.9.
Step-by-step explanation:
In this question, we have to find the 90% confidence interval, using the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 41 - 1 = 40
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.684
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.03 - 0.95 = $8.08.
The upper end of the interval is the sample mean added to M. So it is 9.03 + 0.95 = $9.98.
What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers
$9.98 - $8.08 = $1.9
The difference between these cut-offs is of $1.9.