Final answer:
To determine if the standard deviation is different from two, we can calculate the sample standard deviation of the number of fish in the 15 tanks. Using the provided data, we find that the sample standard deviation is not two.
Step-by-step explanation:
To determine if the standard deviation is different from two, we can calculate the sample standard deviation of the number of fish in the 15 tanks. Using the data provided (11, 10, 9, 10, 10, 11, 11, 10, 12, 9, 7, 9, 11, 10, and 11), we first calculate the mean: (11+10+9+10+10+11+11+10+12+9+7+9+11+10+11)/15 = 154/15 ≈ 10.27. Then, we calculate the squared differences from the mean for each data point: (11-10.27)^2, (10-10.27)^2, (9-10.27)^2, and so on. Summing up the squared differences, we get 12.07. Finally, we divide this sum by the number of data points minus one and take the square root to get the sample standard deviation: sqrt(12.07/14) ≈ 1.13. Since the sample standard deviation is different from two, we can conclude that the standard deviation is different from two at the 5% level of significance.