n order to study the amounts owed to the city council, a city clerk takes a random sample of 16 files from a cabinet containing a large number of delinquent accounts and finds the average amount owed to the city to be $231. It has been claimed that the true mean amount owed on accounts of this type is greater than $250. If it is appropriate to assume that the amount owed is a normally distributed random variable with a standard deviation of $40, then the value of the test statistic appropriate for testing the claim is
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)(You can use n for simplicity.)
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score.
0.246?
To test the claim that the true mean amount owed on accounts of this type is greater than $250, we can use a one-sample t-test. The test statistic in this case is the t-statistic.
The formula for the t-statistic is given by:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case:
Sample mean (x̄) = $231
Population mean (μ) = $250
Sample standard deviation (s) = $40
Sample size (n) = 16
Calculating the t-statistic:
t = ($231 - $250) / ($40 / sqrt(16))
t = (-$19) / ($40 / 4)
t = -$19 / $10
t = -1.9
Therefore, the value of the test statistic appropriate for testing the claim is -1.9.
To determine the value of the test statistic appropriate for testing the claim, we use the following formula:
test statistic = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Given information:
- Sample mean (x̄) = $231
- Population mean (μ) = $250
- Population standard deviation (σ) = $40
- Sample size (n) = 16
Plugging in the values into the formula:
test statistic = ($231 - $250) / ($40 / sqrt(16))
To calculate the denominator, we divide the sample standard deviation by the square root of the sample size:
test statistic = ($231 - $250) / ($40 / 4)
Simplifying the expression further:
test statistic = ($231 - $250) / ($10)
test statistic = (-$19) / ($10)
test statistic = -1.9
Therefore, the value of the test statistic appropriate for testing the claim is -1.9.