How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on sea surface temperatures and coral growth per year at locations in the Red Sea.
Here are the data:
Sea surface temperature 29.71 29.84 30.31 29.66 30.47 30.64 30.93
Growth 2.63 2.58 2.61 2.47 2.27 2.39 2.26
Use your calculator to find:
The mean (± 0.0001) and standard deviation (± 0.0001) for sea surface temperature:
x¯¯¯=____ sx=_____
The mean (±0.0001) and standard deviation (± 0.0001) for coral growth:
y¯¯¯=______ sy=______
The correlation (± 0.0001)r =______
The slope (± 0.01) of the equation of the least-squares regression line is b =_____
and the intercept is (± 0.01) a =_____
To find the mean and standard deviation for sea surface temperature and coral growth, you can use a calculator or a spreadsheet program, such as Microsoft Excel. Here's how you can do it:
1. For sea surface temperature:
- Add up all the temperature values: 29.71 + 29.84 + 30.31 + 29.66 + 30.47 + 30.64 + 30.93 = 211.96
- Divide the sum by the number of values (7 in this case): 211.96 / 7 = 30.28 (mean)
- To find the standard deviation, calculate the sum of the squared differences from the mean:
- Subtract the mean from each temperature value and square the result.
- For example, for the first value, (29.71 - 30.28)^2 = 0.0033281.
- Repeat this for each value and sum up the squared differences.
- Divide the sum by (n-1) (where n is the number of values) and take the square root to get the standard deviation.
2. For coral growth:
- Add up all the growth values: 2.63 + 2.58 + 2.61 + 2.47 + 2.27 + 2.39 + 2.26 = 17.21
- Divide the sum by the number of values (7 in this case): 17.21 / 7 = 2.4571 (mean)
- To find the standard deviation, calculate the sum of the squared differences from the mean and follow the same procedure as for sea surface temperature.
3. To calculate the correlation (r) of the sea surface temperature and coral growth, you can use the CORREL function in Excel or a statistical calculator. This will give you a value between -1 and 1, which indicates the strength and direction of the relationship.
4. To find the slope and intercept of the least-squares regression line, you can use the LINEST function in Excel or a linear regression calculator. This will give you the equation of the line and the slope (b) and intercept (a) values.
Please note that the calculations provided above are examples of how you can find the mean, standard deviation, correlation, slope, and intercept. The actual values may be different depending on the exact calculations and rounding you choose to use.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, I will start you out.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.