Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. A random sample of Arizona bighorn sheep gave the following information: x y 1 17.0 2 18.9 3 19.3 4 19.6 5 20.0 a). Draw a scatter diagram. b). From the scatter diagram, using your intuition, are there linear correlation between x and y? If yes, is the correlation positive or negative? c). Draw a table (as described in class) to find n, ? x, ? y, ? x2, ? y2, ? xy, x ̄, y ̄
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. A random sample of Arizona bighorn sheep gave the following information:
x y
1 17.02 18.9
3 19.3
4 19.6
5 20.0
a). Draw a
b). From the scatter diagram, using your intuition, are there
c). Draw a table (as described in class) to find n, ? x, ? y, ? x2, ? y2, ? xy, x ̄, y ̄
d). Use your result in part (c) to find the correlation coefficient r (to 4 decimal places).
e). Explain what the correlation coefficient r means in the context of the problem.
f). Find the coefficient of determination r2 (to 4 decimal places).
g). Explain what the coefficient of determination r2 means in the context of the problem.
h). Does your interpretation derived in part (f) corresponds to your intuition in part (b)?
i). Find the equation of the least-squares line yˆ = a + bx.
j). Use your result in part (i) to find the mortality rate for a 18 years old bighorn sheep (to 4 decimal places).
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