Probability Assignment
In Assignment #1, the basketball survey, why should you be dubious of the statistical results? Were you consistent with others in gathering the data, and what could be done to improve this sort of observational data gathering?
Regarding Assignment #2, Individual Sports Analysis, what where some limitations encountered and what other analytical ideas occurred to you while working on it?
If the probability of an athlete scoring a point is 23%, about how many attempts (sample size) should be made to validate this probability? (see “More Information” below)
36
42
80
63
LeBron James has a 75% probability of making a free throw. How many free throws would LeBron attempt to validate this success rate?
8
2
80
63
Correlating a player’s points scored to games won provides insight to their contribution to winning games (presumably, the higher the correlation the more effective the player). If a decision requires to recruit one of two players, either player A or player B, and the players correlation between points per game and wins results in:
Player A Player B
Correlation (r) .67 .63
R-Squared (R2) .41 .56
Select:
Player B because although the correlation is lower, the higher R-Squared suggest a tighter fit and a closer relationship between the player and wins
Player A because of the higher correlation and the lower R-Squared
It doesn’t matter, because the skill level of the players is about the same.
Consider the following scatterplot of results of the Gator Basketball game scores as of February 19, 2002 (with Opponent’s scores as x and Florida’s scores as y). What is the best description between Florida’s scores and their opponent’s scores?
There is no real relationship between x and y in this scatterplot.
There is a strong, positive linear relationship between x and y.
There is a strong, negative linear relationship between x and y.
There is a strong, curved relationship between x and y.
In judging the sets of graphs below just by the r (correlation coefficient), preference may be given to graph “b” with a higher r. When the R2 is considered, graph “a” would be preferred because of the tighter relationship between of the correlated numbers.
a. b.
r = .95 R2 = .94 r = .98 R2 = .63
A manufacturer of balloons claims that p, the proportion of its balloons that burst when inflated to a diameter of up to 12 inches, is no more than 0.05. Customers complain that balloons are bursting more frequently.
If the customers want to conduct an experiment to test the manufacturer’s claim, which of the following hypotheses would be appropriate?
H0: p 0.05, Ha: p = 0.05
H0: p = 0.05, Ha: p > 0.05
H0: p = 0.05, Ha: p 0.05
H0: p = 0.05, Ha: p < 0.05
H0: p < 0.05, Ha: p = 0.05
The manufacture assumes that 5% will fail, this means:
1 standard deviation will not fail
2 standard deviations will not fail
.5 standard deviation will not fail
3 standard deviations will not fail
