Final answer:
To determine whether the standard deviation is different from two, calculate the sample standard deviation using the fish counts from the 15 other 20-gallon tanks and compare the result to the claimed standard deviation.
Step-by-step explanation:
The question is about determining whether the standard deviation of the number of fish in 20-gallon tanks is different from the stated value of two, based on a sample data set. To answer this, we calculate the sample standard deviation using the given data: 11; 10; 9; 10; 10; 11; 11; 10; 12; 9; 7; 9; 11; 10; and 11.
Calculating Sample Standard Deviation:
Find the mean (average) number of fish in the sample tanks.
Subtract the mean from each data point to find the deviation of each data point.
Square each deviation to find the squared deviations.
Sum the squared deviations.
Divide this sum by one less than the number of data points (n - 1) for sample standard deviation (since this is a sample, not a population).
Take the square root of that result to obtain the sample standard deviation.
Performing these steps with the provided data will yield whether the sample standard deviation significantly deviates from the claimed standard deviation of two. If the calculated sample standard deviation is far from two, it suggests that the original claim might be incorrect.