wo subspecies of dark-eyed juncos were studied by D. Cristol et al. One of the subspecies migrates each year, and the other does not. Several characteristics of 14 birds of each subspecies were measured, one of which was wing length (in millimeters). The summaries of two samples are as follows: migratory subspecies has a sample mean wing length of 82.1 millimeters with standard deviation of 1.5 millimeters; non-migratory subspecies had a sample mean wing length of 84.92 millimeters with standard deviation of 1.69 millimeters. Assume that wing lengths in populations of subspecies are normally distributed. Conduct a hypothesis test to determine if there is a significant difference between mean wing lengths of the two subspecies. a. The appropriate hypotheses are b. Degree of freedom, test statistic and p-value are c. At the significance level calculated in part (b), we conclude that: i. The difference between mean wing lengths of the two subspecies is statistically significant ii. The difference between mean wing lengths of the two subspecies is not statistically significant
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Two subspecies of dark-eyed juncos were studied by D. Cristol et al. One of the subspecies migrates each year, and the other does not. Several characteristics of 14 birds of each subspecies were measured, one of which was wing length (in millimeters). The summaries of two samples are as follows: migratory subspecies has a sample mean wing length of 82.1 millimeters with standard deviation of 1.5 millimeters; non-migratory subspecies had a sample mean wing length of 84.92 millimeters with standard deviation of 1.69 millimeters. Assume that wing lengths in populations of subspecies are
a. The appropriate hypotheses are
b. Degree of freedom, test statistic and p-value are
c. At the significance level calculated in part (b), we conclude that:
- i. The difference between mean wing lengths of the two subspecies is statistically significant
- ii. The difference between mean wing lengths of the two subspecies is not statistically significant
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