Question

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
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

The sample mean of 3126.1 meters for the depth measurements at specific locations in northeast Greenland National Park is below 3140 meters. However, to confirm that the Greenland ice sheet's average depth is statistically significantly below 3140 meters, more data and a standard deviation are needed to perform a comprehensive hypothesis test.

Step-by-step explanation:

To determine if there is enough evidence that the average depth of the Greenland ice sheet is below 3140 meters, we can perform a simple statistical analysis using the given data. The data collected on the depths measured during summer months in the northeast Greenland National Park are as follows: 3115, 3133, 3123, 3145, 3125, 3131, 3127, 3120, 3118, 3124.

First, we calculate the sample mean (average) of the depths:

`\(\text{Mean} = (3115 + 3133 + 3123 + 3145 + 3125 + 3131 + 3127 + 3120 + 3118 + 3124)/(10) = 3126.1\,\text{m}\)`

The sample mean of 3126.1 meters is indeed lower than 3140 meters. To establish if this difference is statistically significant, one would typically perform a hypothesis test, such as a one-sample t-test.

However, the provided data does not include a standard deviation or the size of the total population that the data represents, which are necessary to calculate the t-statistic and the corresponding p-value to assess significance. Without such information, we can only state that the sample mean is less than 3140m based on the given measurements.

Considering the assumption that the depth is normally distributed, the indication is that the depth measurements at these locations are below 3140 meters. To make a more robust conclusion about the average depth throughout Greenland's ice sheet, additional data and a proper hypothesis testing framework would be required.