Assignment 5 - Admission/Application Essay Example

Unit Fill in the following prob(hit/3 misses) prob(hit/2 misses) p(hit miss) p(hit) p(hit/1hit) p(hit/2 hits p(hit/3 hits) ρ0.83330.70.583330.520.40760.50.5-0.08606 2. Do your conditional probabilities show evidence of the hot hand? Explain.There is no evidence of hot hand. Looking at the above conditional probabilities, a player has higher percentage of making a hit after making a miss (or last several misses) and in comparison a player has a lower chance of making a hit after making their last hit.

The player’s probability of a hit is essentially lower following a hit (weighted calculation=40.76%) than following a miss (weighted calculation=58.3%), this basically contradicts the hot hand hypothesis.3. Does your correlation coefficient ρ show evidence of the hot hand? Explain.For the range of data the correlation coefficient is negative. The correlation coefficient therefore does not show evidence of the hot hand. The probability of a hit given a hit is 40.76%, but the probability of a hit given several previous hit remains constant at 50%.

Hence there is no evidence of significant positive correlation between successive shots.Given a player has made one or two hits; the other competing team will obviously intensify their defensive mechanism on the particular player and hence take away the players potential successive hits. A team’s defensive strategy is probably a major factor responsible for the negative correlation between successive hits.4. Fill in the following.Wald-Wolfowitz runs testProbability of observing 50 or fewer runs while 47.

5 were expected (standard deviation (50) = 4.7664)Z-value= 0.5312p: 0.29764; 1-p= 0.70236c.c .z-value = 0.6361p: 0.2624; 1-p= 0.7376Exact probability of 50or fewer runsp: 0.26273; 1-p= 0.73727hits misses runs expected runs z-statistic52 48 50 47.5 0.53125. Show where your runs number falls on the distribution.Given our z value is 0.5312, we use extrapolation method to gauge the percentage value and then refer to the distribution above. Z value of 0.5224 has a percentage of 30%, while a Z value of 0.

6745 has a percentage 25%.Since this is a two tailed distribution, The runs number falls in the13.6% distribution section. This is the 1 to 2 and -2 to 1 section.6. Is this evidence of the hot hand? Explain. There is evidence of existence of hot hand. The Z statistic reported above test the significance of the variation between the expected and the observed number of runs. There always a significant difference between the expected value and observe value for individual player’s. Run tests performed on each player within individual games reveal compelling results.

Placing into consideration both the 76ers and their competitors, data obtained of 727 individual players game records presented more than two runs. When the observed number of runs and expected number of runs are compared there is no sufficient to provide any basis for rejecting the hot hand hypothesis. Clearly 13.55% calculated is less than 13.6% tabulated therefore we accept the null hypothesis.ReferencesReifman, Alan. Hot Hand: The Statistics Behind Sports Greatest Streaks. Washington, D.C: Potomac Books, 2011. Print.