91Ó°ÊÓ

A local golf pro wanted to compare two styles of golf club. One golf club had a graphite shaft and the other had a steel shaft. It is believed that graphite shafts allow a player to hit the ball farther, but the manufacturer of the new steel shaft said the ball travels just as far with its new technology. To test this belief, the pro recruited 10 golfers from the driving range. Each player was asked to hit one ball with the graphite-shafted club and one ball with the new steel-shafted club. The distance that the ball traveled was determined using a range finder. A coin flip was used to determine whether the player hit with the graphite club or the steel club first. Results indicated that the distance the ball was hit with the graphite club was no different than the distance when using the steel club. (a) What type of experimental design is this? (b) What is the response variable in this study? (c) What is the factor that is set to predetermined levels? What is the treatment? (d) Identify the experimental units. (e) Why did the golf pro use a coin flip to determine whether the golfer should hit with the graphite first or the steel first? (f) Draw a diagram similar to Figure \(7,8,\) or 10 to illustrate the design.

Step by step solution

01

Identify the Experimental Design

This study employs a paired design where the same subjects (golfers) are exposed to both treatments (graphite-shafted club and steel-shafted club). Each golfer's performance with the two types of clubs is compared directly.

02

Determine the Response Variable

The response variable in this study is the distance the ball travels when hit with either the graphite or steel-shafted golf club. This distance is the primary data being collected.

03

Identify the Factor and Treatment

The factor in this study is the type of golf club shaft, which is set to two predetermined levels: graphite and steel. The treatment is the specific type of club shaft used by the golfers for hitting the ball.

04

Identify the Experimental Units

The experimental units in this study are the 10 golfers recruited to participate in this experiment. Each golfer serves as an individual unit receiving both treatments.

05

Explain the Use of a Coin Flip

A coin flip was used to randomly decide the order in which each golfer hit with the graphite or steel club first. This randomization helps to prevent any order effects or biases that may influence the distance the ball travels.

06

Illustrate the Design

A diagram of the study design could be envisioned as follows:1. Recruit 10 golfers.2. Perform a coin flip to randomly assign the hitting order (graphite first vs. steel first).3. Collect data on the distance the ball travels for each club per golfer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

response variable

In this experiment, the response variable is what the researcher wants to measure or observe. For the golf club study, the response variable is the distance the golf ball travels. This is important because it answers the main question: Does the type of club (graphite vs. steel) affect how far the ball goes? By focusing on the distance, the researcher can determine if there's a significant difference between the two types of clubs.

randomization

Randomization is a crucial aspect of experimental design. It helps remove bias and ensures each subject receives treatments in a random order. In our golf club study, the coin flip to decide if a golfer uses the graphite or steel shaft first is an example of randomization. This method ensures that the order of using the clubs doesn't influence the results. It's like giving both clubs a fair chance without any kind of favoritism.

paired design

A paired design involves comparing two treatments using the same subjects. In this study, each golfer uses both the graphite and steel clubs. This type of design is powerful because it controls for individual differences among golfers, like their skill level. By having each golfer use both clubs, the comparison is more accurate since each golfer serves as their own control. It’s like taking two measurements from the same person under different conditions.

treatment levels

Treatment levels refer to the different conditions applied to the subjects in the experiment. Here, we have two levels: the graphite-shafted club and the steel-shafted club. These are the different conditions (or treatments) that golfers are exposed to. The purpose is to evaluate the effect of each treatment level (club type) on the response variable (distance). These levels help in understanding if a specific treatment (type of club shaft) works better.

experimental units

Experimental units are the subjects being studied. In this case, the 10 golfers are the experimental units. Each golfer hits with both types of clubs, making them the focus of observation. This concept is essential because the characteristics of these units (golfers) can affect the experiment's outcome. By carefully choosing experimental units and managing how they are treated, researchers can ensure that the results are reliable and valid.