Question

problem 9.1. the greenland ice sheet covers roughly 80% of the surface of greenland, being the second largest body of ice in the world, after the antarctic ice sheet. as the arctic climate is rapidly warming, the greenland ice sheet has experienced record melting in the recent years. the following data gives the depth of the ice sheet (in m) measured at various locations during the summer months in the northeast greenland national park: 3115 3133 3123 3145 3125 3131 3127 3120 3118 3124 3115 3133 3123 3145 3125 3131 3127 3120 3118 3124 using this data, is there enough evidence that the average depth of the ice sheet is below 3140m? assume that the depth of the ice sheet is normally distributed.

Answer 1

To determine if the average depth of the Greenland ice sheet is below 3140m, a hypothesis test can be performed using a one-sample t-test. Steps include calculating sample mean and standard deviation, defining a significance level, calculating the t-value using a formula, finding critical t-values, and comparing the calculated t-value to the critical t-value(s).

Step-by-step explanation:

To determine whether there is enough evidence that the average depth of the Greenland ice sheet is below 3140m, we can perform a hypothesis test. The null hypothesis, denoted as H0, is that the average depth is equal to or greater than 3140m. The alternative hypothesis, denoted as H1, is that the average depth is below 3140m. We can use a one-sample t-test to analyze the given data and assess the evidence.

Steps to perform the hypothesis test:

1. Calculate the sample mean and the sample standard deviation from the given data.
2. Define the significance level (α) for the test. Commonly used values are 0.05 and 0.01.
3. Assuming the null hypothesis is true, calculate the t-value using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
4. Calculate the degrees of freedom (df) for the t-distribution, which is equal to the sample size minus 1.
5. Find the critical t-value(s) from the t-distribution table or using statistical software, based on the significance level and degrees of freedom.
6. Compare the calculated t-value with the critical t-value(s). If the calculated t-value falls within the rejection region (i.e., it is less than the critical t-value), we reject the null hypothesis and conclude that there is enough evidence that the average depth is below 3140m. Otherwise, we fail to reject the null hypothesis.

Performing these steps will allow us to determine whether there is sufficient evidence to support the claim that the average depth of the ice sheet is below 3140m.