Final answer:
To determine if the average depth of the Hudson Bay has increased, a hypothesis test is conducted using the sample mean, population variance, and the significance level. The calculated Z-value is 1.69. Rejecting the null hypothesis suggests that the average depth has increased, but the cause is not addressed in the given information.
Step-by-step explanation:
To determine if the average depth of the Hudson Bay has increased, we can conduct a hypothesis test using the given sample mean, population variance, and the significance level of 0.05.
Let's state our hypotheses:
- Null hypothesis (H0): The average depth has not increased (μ = 305 feet)
- Alternative hypothesis (H1): The average depth has increased (μ > 305 feet)
To calculate the Z-value, we will use the formula: Z = (sample mean - population mean) / (population standard deviation / √ sample size)
In this case, the sample mean is 306.2 feet, the population mean is 305 feet, the population variance is 3.6, and the sample size is 55. Plugging in these values gives us Z = (306.2 - 305) / (sqrt(3.6) / sqrt(55)) ≈ 1.69.
Using a Z-table or calculator, we find that the critical Z-value for a significance level of 0.05 (one-tailed test) is approximately 1.645. Since the calculated Z-value (1.69) is greater than the critical Z-value, we reject the null hypothesis.
Therefore, we can conclude that there is evidence to suggest that the average depth of the Hudson Bay has increased. However, the given information does not provide evidence regarding the cause of this increase.