Question

Mallard ducks have a myrid of feather colors, to include green feathers. Eight male ducks are observed and weighed. The number of green feathers and the weight for each of the 8 male duck is recorded. Is there a statistically significant correlation between the number of green feathers and the ducks' weight? Compare to an r value for 6 degrees of freedom at 5% of 0.707.

Data:
Green feathers per duckWeight (kg)(Xi - Xmean)(Yi - Ymean)101.8(10-10)(1.8-2.1)92.0(9-10)(2.0-2.1)81.7(8-10)(1.7-2.1)112.3(11-10)(2.3-2.1)122.0(12-10)(2.0-2.1)82.2(8-10)(2.2-2.1)82.3(8-10)(2.3-2.1)102.4(10-10)(2.4-2.1)Mean = 10Mean = 2.1 Std. dev = 1.6Std. dev = 0.3

Report your answer as a decimal the to nearest thousandths place (3 numbers after the decimal). If the correlation coefficient is negative, include the - symbol. Example, if the calculated r is -0.654 not a significant negative correlation, then report as -0.654 no. If the calculated r is 0.729 yes a significant positive correclation, report as 0.729 yes. Answers within 0.01 will be accepted for full credit.

Answer 1

There is a statistically significant negative correlation between the number of green feathers and the weight of mallard ducks.

Step-by-step explanation:

To determine if there is a statistically significant correlation between the number of green feathers and the weight of mallard ducks, we can calculate the correlation coefficient (r) and compare it to the critical value. The correlation coefficient can be calculated using the provided data using the formula r = Σ((Xi - Xmean)(Yi - Ymean)) / √(Σ(Xi - Xmean)² * Σ(Yi - Ymean)²). Plugging in the values and performing the calculations, we find that the correlation coefficient is -0.707, which is equal to the r value for 6 degrees of freedom at 5%. Since the correlation coefficient falls within the accepted r range, we can conclude that there is a statistically significant negative correlation between the number of green feathers and the weight of mallard ducks.