Once per day, over a period of 10 days, a sprinting coach times two sprinters wh

Question

Once per day, over a period of 10 days, a sprinting coach times two sprinters while they run 100 meters. He obtains the following times (in seconds):

            Carl:               10.2, 10.3, 10.2, 10.4, 10.3, 10.3, 10.2, 10.4, 10.3, 10.5

            Poindexter:   10.4, 10.5, 10.3, 10.4, 10.3, 10.5, 10.3, 10.4, 10.5, 10.4

            Samuel:         10.1, 10.2, 10.2, 10.5, 10.1, 10.3, 10.4, 10.3, 10.3, 10.4

The precision of each measurement is 0.1 seconds.

Later, he ponders the following three statements:

            1. There is a significant difference between the times of Carl and Poindexter.

            2. There is a significant difference between the times of Poindexter and Samuel.

            3. There is a significant difference between the times of Samuel and Carl.

According to the criteria laid out in Appendix 2 of the Lab Manual, the answers to these questions are

            A. 1. Yes; 2. Yes; 3. Yes

            B. 1. Yes; 2. Yes; 3. No

            C. 1. Yes; 2. No; 3. No

            D. 1. No; 2. No; 3. No

Explanation / Answer

By using R software we twst it as folows ,

COmmnds and output :

> x=c(10.2,10.3,10.2,10.4,10.3,10.3,10.2,10.4,10.3,10.5)
> p=c(10.4,10.5,10.3,10.4,10.3,10.5,10.3,10.4,10.5,10.4)
> s=c(10.1,10.2,10.2,10.5,10.1,10.3,10.4,10.3,10.3,10.4)
> # TO check there is significsnt difference between Carls and poindexter
> t.test(x,p)

Welch Two Sample t-test

data: x and p
t = -2.2119, df = 17.343, p-value = 0.04066
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.175716111 -0.004283889
sample estimates:
mean of x mean of y
10.31 10.40

> # TO check there is significsnt difference between poinxtender and samuel.
> t.test(p,s)

Welch Two Sample t-test

data: p and s
t = 2.4495, df = 15.031, p-value = 0.02704
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.01559943 0.22440057
sample estimates:
mean of x mean of y
10.40 10.28

> # TO check there is significsnt difference between samual and carls
> t.test(x,s)

Welch Two Sample t-test

data: x and s
t = 0.57499, df = 16.748, p-value = 0.5729
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.08020601 0.14020601
sample estimates:
mean of x mean of y
10.31 10.28

INTERPRETATION:

1. There is a significant difference between the times of Carl and Poindexter.

            2. There is a significant difference between the times of Poindexter and Samuel.

            3. There is a no significant difference between the times of Samuel and Carl.

Option   B. 1. Yes; 2. Yes; 3. No is correct

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