Math / Data & Statistics

QuestionShort Answer
25. (12 points total) We wish to compare reaction time to sound with reaction time to light. In a carefully controlled experiment, the time required to react to a buzzer and the time required to react to a white signal light are obtained for six subjects. Below are the results (in milliseconds): \begin{tabular}{lrrrrrr} \hline Subject & 1 & 2 & 3 & 4 & 5 & 6 \\ Light & 39 & 37 & 44 & 42 & 43 & 41 \\ Buzzer & 35 & 37 & 38 & 41 & 39 & 40 \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We're checking if people react faster to sound (a buzzer) or light, by comparing reaction times of six people. Watch out! Don't mix up the light and buzzer times!
Make sure you're comparing the differences correctly.

STEP 2

1. Calculate the difference for each person.
2. Calculate the average difference.

STEP 3

We want to see how much faster or slower each person is to light versus sound.
A positive difference means they were faster to react to sound.
A negative difference means they were faster to react to light.

STEP 4

$\text{Buzzer} - \text{Light} = 35 - 39 = -4$ Subject 1 reacted $-4$ milliseconds faster to the light.

STEP 5

$\text{Buzzer} - \text{Light} = 37 - 37 = 0$ Subject 2 reacted the same speed to both!

STEP 6

$\text{Buzzer} - \text{Light} = 38 - 44 = -6$ Subject 3 reacted $-6$ milliseconds faster to the light.

STEP 7

$\text{Buzzer} - \text{Light} = 41 - 42 = -1$ Subject 4 reacted $-1$ millisecond faster to the light.

STEP 8

$\text{Buzzer} - \text{Light} = 39 - 43 = -4$ Subject 5 reacted $-4$ milliseconds faster to the light.

STEP 9

$\text{Buzzer} - \text{Light} = 40 - 41 = -1$ Subject 6 reacted $-1$ millisecond faster to the light.

STEP 10

Let's add all those differences together!
This tells us the total difference across all the subjects. $-4 + 0 + (-6) + (-1) + (-4) + (-1) = -16$

STEP 11

We have 6 subjects, so we'll divide the total difference by 6 to get the average difference. $\frac{-16}{6} = -\frac{8}{3} \approx -2.67$

STEP 12

On average, people reacted around $2.67$ milliseconds faster to light than to sound.

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Studdy Solution

STEP 1

What is this asking? We're checking if people react faster to sound (a buzzer) or light, by comparing reaction times of six people. Watch out! Don't mix up the light and buzzer times!
Make sure you're comparing the differences correctly.

STEP 2

1. Calculate the difference for each person.
2. Calculate the average difference.

STEP 3

We want to see how much faster or slower each person is to light versus sound.
A positive difference means they were faster to react to sound.
A negative difference means they were faster to react to light.

STEP 4

$\text{Buzzer} - \text{Light} = 35 - 39 = -4$ Subject 1 reacted $-4$ milliseconds faster to the light.

STEP 5

$\text{Buzzer} - \text{Light} = 37 - 37 = 0$ Subject 2 reacted the same speed to both!

STEP 6

$\text{Buzzer} - \text{Light} = 38 - 44 = -6$ Subject 3 reacted $-6$ milliseconds faster to the light.

STEP 7

$\text{Buzzer} - \text{Light} = 41 - 42 = -1$ Subject 4 reacted $-1$ millisecond faster to the light.

STEP 8

$\text{Buzzer} - \text{Light} = 39 - 43 = -4$ Subject 5 reacted $-4$ milliseconds faster to the light.

STEP 9

$\text{Buzzer} - \text{Light} = 40 - 41 = -1$ Subject 6 reacted $-1$ millisecond faster to the light.

STEP 10

Let's add all those differences together!
This tells us the total difference across all the subjects. $-4 + 0 + (-6) + (-1) + (-4) + (-1) = -16$

STEP 11

We have 6 subjects, so we'll divide the total difference by 6 to get the average difference. $\frac{-16}{6} = -\frac{8}{3} \approx -2.67$

STEP 12

On average, people reacted around $2.67$ milliseconds faster to light than to sound.

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Studdy Solution

STEP 1

What is this asking? We're checking if people react faster to sound (a buzzer) or light, by comparing reaction times of six people. Watch out! Don't mix up the light and buzzer times!Make sure you're comparing the *differences* correctly.

STEP 2

1. Calculate the difference for each person.2. Calculate the average difference.

STEP 3

We want to see how much faster or slower each person is to light versus sound.A positive difference means they were faster to react to sound.A negative difference means they were faster to react to light.

STEP 4

Buzzer−Light=35−39=−4\text{Buzzer} - \text{Light} = 35 - 39 = -4Buzzer−Light=35−39=−4 Subject 1 reacted −4-4−4 milliseconds *faster* to the light.

STEP 5

Buzzer−Light=37−37=0\text{Buzzer} - \text{Light} = 37 - 37 = 0Buzzer−Light=37−37=0 Subject 2 reacted the same speed to both!

STEP 6

Buzzer−Light=38−44=−6\text{Buzzer} - \text{Light} = 38 - 44 = -6Buzzer−Light=38−44=−6 Subject 3 reacted −6-6−6 milliseconds *faster* to the light.

STEP 7

Buzzer−Light=41−42=−1\text{Buzzer} - \text{Light} = 41 - 42 = -1Buzzer−Light=41−42=−1 Subject 4 reacted −1-1−1 millisecond *faster* to the light.

STEP 8

Buzzer−Light=39−43=−4\text{Buzzer} - \text{Light} = 39 - 43 = -4Buzzer−Light=39−43=−4 Subject 5 reacted −4-4−4 milliseconds *faster* to the light.

STEP 9

Buzzer−Light=40−41=−1\text{Buzzer} - \text{Light} = 40 - 41 = -1Buzzer−Light=40−41=−1 Subject 6 reacted −1-1−1 millisecond *faster* to the light.

STEP 10

Let's add all those differences together!This tells us the *total* difference across all the subjects. −4+0+(−6)+(−1)+(−4)+(−1)=−16-4 + 0 + (-6) + (-1) + (-4) + (-1) = -16−4+0+(−6)+(−1)+(−4)+(−1)=−16

STEP 11

We have **6** subjects, so we'll divide the total difference by **6** to get the *average* difference. −166=−83≈−2.67\frac{-16}{6} = -\frac{8}{3} \approx -2.676−16​=−38​≈−2.67

STEP 12

On average, people reacted around 2.672.672.67 milliseconds *faster* to light than to sound.

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What is this asking? We're checking if people react faster to sound (a buzzer) or light, by comparing reaction times of six people. Watch out! Don't mix up the light and buzzer times!
Make sure you're comparing the differences correctly.

1. Calculate the difference for each person.
2. Calculate the average difference.

We want to see how much faster or slower each person is to light versus sound.
A positive difference means they were faster to react to sound.
A negative difference means they were faster to react to light.

$\text{Buzzer} - \text{Light} = 35 - 39 = -4$ Subject 1 reacted $-4$ milliseconds faster to the light.

$\text{Buzzer} - \text{Light} = 37 - 37 = 0$ Subject 2 reacted the same speed to both!

$\text{Buzzer} - \text{Light} = 38 - 44 = -6$ Subject 3 reacted $-6$ milliseconds faster to the light.

$\text{Buzzer} - \text{Light} = 41 - 42 = -1$ Subject 4 reacted $-1$ millisecond faster to the light.

$\text{Buzzer} - \text{Light} = 39 - 43 = -4$ Subject 5 reacted $-4$ milliseconds faster to the light.

$\text{Buzzer} - \text{Light} = 40 - 41 = -1$ Subject 6 reacted $-1$ millisecond faster to the light.

Let's add all those differences together!
This tells us the total difference across all the subjects. $-4 + 0 + (-6) + (-1) + (-4) + (-1) = -16$

We have 6 subjects, so we'll divide the total difference by 6 to get the average difference. $\frac{-16}{6} = -\frac{8}{3} \approx -2.67$

On average, people reacted around $2.67$ milliseconds faster to light than to sound.