Two teams are comparing the speed of their runners. Each team ran a lap around a track, and their time in seconds was recorded. Although not a random sample, we can assume that their times are representative of each team's capabilities. We wish to see if there is evidence that Team 1 is slower (higher time) on average than Team 2. You wish to test the following claim (HaHa) at a significance level of α=0.002 Ho:μ1=μ2 Ha:μ1>μ2 You obtain the following two samples of data. Team #1 Team #2 80.1 76.1 81 81.1 74 76.9 67.3 80.1 90.6 76 77.4 71.9 85.7 69.3 83.5 78.2 82.5 72.1 69.3 81.9 77.6 74.1 78.9 85.7 73.6 86.7 82.5 72.5 83 78.3 80.8 86.7 90.6 74.5 70.9 78.9 74.5 76.9 84 71.1 81 80.6 75.6 74 81 67.3 83 76 75.6 79.8 78.2 71.9 71.4 77 71.9 70.9 71.1 80 73.6 77.4 70.6 79.2 87.3 78 84.9 68.3 56.5 50.2 67.8 66.5 64.2 62.1 75.6 76.4 78.4 71.8 69.5 63.5 71.1 70 76.4 56.5 79.7 72.1 73.9 79.7 78.1 79 71.8 80 79.7 66 71.6 65.4 73 54.3 57.3 83.4 85.9 65.1 64.5 74.2 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value = The p-value is...? less than (or equal to) αα greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to reject that Team 1 is slower (higher time) on average than Team 2. There is not sufficient evidence to reject that Team 1 is slower (higher time) on average than Team 2. There is sufficient evidence to show Team 1 is slower (higher time) on average than Team 2. There is not sufficient evidence to show Team 1 is slower (higher time) on average than Team 2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Two teams are comparing the speed of their runners. Each team ran a lap around a track, and their time in seconds was recorded. Although not a random sample, we can assume that their times are representative of each team's capabilities. We wish to see if there is evidence that Team 1 is slower (higher time) on average than Team 2.

You wish to test the following claim (HaHa) at a significance level of α=0.002

Ho:μ1=μ2
Ha:μ1>μ2

You obtain the following two samples of data.

Team #1

Team #2

80.1	76.1	81	81.1
74	76.9	67.3	80.1
90.6	76	77.4	71.9
85.7	69.3	83.5	78.2
82.5	72.1	69.3	81.9
77.6	74.1	78.9	85.7
73.6	86.7	82.5	72.5
83	78.3	80.8	86.7
90.6	74.5	70.9	78.9
74.5	76.9	84	71.1
81	80.6	75.6	74
81	67.3	83	76
75.6	79.8	78.2	71.9
71.4	77	71.9	70.9
71.1	80	73.6	77.4
70.6	79.2	87.3	78
84.9

68.3	56.5	50.2	67.8
66.5	64.2	62.1	75.6
76.4	78.4	71.8	69.5
63.5	71.1	70	76.4
56.5	79.7	72.1	73.9
79.7	78.1	79	71.8
80	79.7	66	71.6
65.4	73	54.3	57.3
83.4	85.9	65.1	64.5
74.2

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.)
p-value =

The p-value is...?

less than (or equal to) αα
greater than α

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to reject that Team 1 is slower (higher time) on average than Team 2.
There is not sufficient evidence to reject that Team 1 is slower (higher time) on average than Team 2.
There is sufficient evidence to show Team 1 is slower (higher time) on average than Team 2.
There is not sufficient evidence to show Team 1 is slower (higher time) on average than Team 2.

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