The given table from the RLab link is provided below. The second column is Free

Question

The given table from the RLab link is provided below. The second column is Free Throws Made the third column is Free THrows Attempted.

1 3 4 2 5 10 3 2 3 4 0 2 5 6 8 6 3 8 7 5 8 8 1 4 9 0 0 10 5 5 11 4 8 12 0 4 13 3 5 14 2 2 15 0 1 16 3 4 17 0 0 18 3 3 19 5 8 20 9 13 21 2 3 22 7 10 23 3 4 24 1 3 25 0 2 26 3 7 27 3 4 28 2 6 29 8 12 30 1 2 31 6 8 32 1 3 33 1 2 34 5 6 35 4 6 36 0 2 37 0 0 38 2 2 39 0 0 40 2 4 41 3 4 42 3 4 43 2 4 44 1 2 45 2 2 46 5 8 47 4 4 48 3 4 49 4 6 50 4 10 51 3 8 52 3 6 53 6 8 54 4 5 55 3 3 56 6 8 57 1 3 58 2 6 59 4 5 60 1 2 61 5 8 62 2 4 63 4 6 64 0 7 65 2 4 66 14 16 Problem #1, Hack-a-Shaq is a basketball strategy initially instituted in the NBA by the Dallas Mavericks coach Don Nelson to hinder the scoring ability of the opposing team by continuously committing personal fouls against one of its opposing players, the player chosen being the one with the weakest free throw percentage among players on the court. Sorme of the previous victims of this strategy were Shaquille ONcal, Dennis Rodman etc.. and recently there are Dwight Howard, DeAndre Jordan, Andre Drummond, ctc. In particular Mr. Drummond's career free throw percentage is 41.8%. In 2017-2018 season, however, he has shown quite improved daily stats on free throws as follows: Free Throw Made 3 5 2 0 6 3 5 1 05 1 0 3 2 0 3 0 Free Throw Attempt 4 10 3 2 8 8 8 1 0 5 8 4 5 2 1 4 0 Free Throw Made 3 5 9273 1 0 3 3 2 8 1 6 1 1 5 FreeThrowAttempt|38133104327461228326 Free Throw Made 4 0 2 0 2 3 3 2 1 2 5 4 3 4 43 Free Throw Attempt 6 202 044442 2844 6 10 8 Free Throw Free Throw Attempt 6 8 5 3 8 3 6 5 2 8 4 6 7 4 16 Made 3 6 4 3 6 1 2 4 1 5 2 1 0 2 11 This data can be obtained by the following code on RStudio: people.stat.sc.edu/taeho/teaching/1ab/AD_FT.RData" dounload file(http:l destfile "AD.FT.RData");load("AD_FT.RData") Given this data, please answer the following questions to formally test whether he has im- proved his free throw accuracy under 0.01 significance level. 1. Please describe the target parameter and what is the value of the point estimate? 2. Check whether we have enough sample sizes to ensure the normality assumption. 3. State null and alternative hypothesis. 4. Calculate the test statistic, z* 5. Calculate the p-value. 6. Draw your conchusion and provide the interpretation within the context of the problem

Explanation / Answer

1.

Loaded the file AD_FT.RData in R-Studio. The first few records of the dataset can be seen by the head() command.

> head(AD_FT.RData)
Sno FreeThrowsMade FreeThrowsAttempted
1 1 3 4
2 2 5 10
3 3 2 3
4 4 0 2
5 5 6 8
6 6 3 8

We are interested in free throw pecentage which is the proportion of FreeThrowsMade over FreeThrowsAttempted. So, the target parameter is mean free throw pecentage.

Calculate the mean free throw pecentage with the below command in R-studio.

mean(AD_FT.RData$FreeThrowsMade / AD_FT.RData$FreeThrowsAttempted, na.rm = "TRUE")

We have used na.rm = "TRUE" parameter to omit rows with values NaN for FreeThrowsMade = FreeThrowsAttempted = 0. (Rows 9, 17, 37, 39)

The point estimate of mean free throw pecentage is 0.5814

2.

For normality assumption np > 5 and n(1-p) > 5

Here n = 66, p = 0.418

66 * 0.418 = 27.588 which is greater than 5

66 * (1-0.418) = 38.412   which is greater than 5

So, the normality assumption is satisfied.

3.

H0: Mean free throw pecentage, p = 41.8%

Ha: Mean free throw pecentage, p > 41.8%

4.

Standard error of the proportion, ? = sqrt[ P * ( 1 - P ) / n ] = sqrt[0.418 * ( 1 - 0.418 ) / 66 ] = 0.0607

Test statistic, z = (0.5814 - 0.418)/0.0607 = 2.69

5.

P-value = P(z > 2.69) = 0.0036

6.

As, p-value is less than the significance level (0.01), we reject the null hypothesis and conclude that there is significant evidence that mean free throw pecentage is greater than 41.8%.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.