Q 8.92. - Elementary Statistics

Question

Long Drives. The Professional Golfer's Association of America (PGA) organizes golf tournaments for professional golfers. The following table lists the longest drives, in yards, recorded during a PGA tournament for a random sample of $26$ golfers. Use the technology of your choice to decide whether applying the $z-$interval procedure to these data is reasonable. Explain your answer. 

Step-by-Step Solution

Answer

The applying $z-$interval procedure to the given data is not reasonable.

Step 1: Given information

395	400	377	367	386	407	383
396	371	376	373	384	369	391
386	393	374	366	388	371	416
375	450	370	379	381

Step 2: Explanation

Check whether using the z-interval technique on the given data is appropriate.

Draw the normal probability plot for golfers using MINITAB.

Procedure for MINITAB:

Step 1: Select Probability Plot from the Graph menu.

Step 2: Click OK after selecting Single.

Step 3: In the Graph variables section, type Golfers in the column.

Step 4: Click the OK button.

OUTPUT FROM MINITAB: 

Draw the histogram for golfers using MINITAB.

Procedure for MINITAB:

Step 1: Select Histogram from the Graph menu.

Step 2: Click OK after selecting Simple.

Step 3: In the Graph variables section, type in the Golfers column.

Step 4: Click the OK button.

OUTPUT FROM MINITAB: 

Step 3: Explanation

The following are the conditions for using the $z-$interval procedure: 

Small Sample size:

The $z-$interval approach is employed when the sample size is less than 15 and the variable is normally distributed or extremely near to being normally distributed.

Moderate Sample size: 

When the sample size is between $15$ and $30$ and the variable is not normally distributed or there is no outlier in the data, the $z-$interval technique is performed.

Large Sample size: 

The $z-$interval technique is utilized without restriction if the sample size is bigger than $30$

The distribution of the variable is extremely skewed, and the sample size $(=26)$ is lower, as shown by the MINITAB result. As a result, the distribution of Golfers deviates from the normal. As a result, applying the $z-$interval technique to the given data is illogical.