Question

In: Statistics and Probability

Predictive sports analytics is one of the biggest priorities of professional sports teams, including within the...

Predictive sports analytics is one of the biggest priorities of professional sports teams, including within the NBA, where teams analyze real-time stats of players. Shots per game is a particularly meaningful metric for determining a player's level of confidence, as players tend to take more shots when they are feeling confident. Kawhi Leonard had the following shot attempts during the 6-game NBA finals:

Shot Attempts: 19,23,26,25,22,25

Kawhi's average (mean) number of shots attempted during the past 5 seasons is 16.0. Assuming the data looks approximately normal, perform the appropriate hypothesis test to see if the number of shots Kawhi took during the NBA finals is greater from his average. Test the claim using a 1% level of significance.

a. What are the correct hypotheses?

b. Based on the hypothesis, find the
Test Statistic?
P Value?

c. Choose one of the following:
Reject Null Hypothesis
Fail to Reject Null Hypothesis
Accept Null Hypothesis
Accept Alternative Hypothesis

d. Calculate the 99% confidence interval for estimating the mean number of shots per game of all of Kawhi's games.

Solutions

Expert Solution

: Kawhi's Mean number of shots per game

To Test if the number of shots Kawhi took during the NBA finals is greater from his average

Null hypothesis : Ho : = 16

Alternate hypothesis : Ha: > 16

Right tailed test

Sample data :

xi : Number of shot attempts in ith game

x: (19,23,26,25,22,25)

Sample size : n= 6

Sample mean number of shots per game :

Sample standard deviation : s

Hypothesized mean : = 16

Test Statistic = 6.9569

Degrees of freedom = n-1 =6-1=5

For right tailed test :

For 5 degrees of freedom P(t>6.9569) =0.0005

p-value = 0.0005

c. Choose one of the following:

As P-Value i.e. is less than Level of significance i.e (P-value:0.0005 < 0.01:Level of significance); Reject Null Hypothesis

Reject Null Hypothesis

d. Calculate the 99% confidence interval for estimating the mean number of shots per game of all of Kawhi's games

Formula for Confidence Interval for Population mean when population Standard deviation is not known

for 99% confidence level = (100-99)/100 =0.01

/2 = 0.01/2=0.005

t/2,n-1 = t0.005,5 = 4.0321

99% confidence interval for estimating the mean number of shots per game of all of Kawhi's games

99% confidence interval for estimating the mean number of shots per game of all of Kawhi's games

(19.0864,27.5802)

orchestra answered 1 year ago

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