Question

This question has Z parts. Each of the 7 parts (Part A - Part G) has a dropdown list of possible answers. Choose the best answer from the dropdown list for EACH part of the question below. A researcher is interested in whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. He classifies participants into three transportation groups (those who: bike/walk, take public transit or drive) and asks them how they typically feel on a normal Monday morning: happy/excited, angry/irritated, or sleepy. Data from his survey on 200 participants are presented below. Happy/excited Angry/irritated Sleepy TOTAL Bike/walk 22 6 12 40 Public transit 18 6 36 60 Drive 20 18 62 100 TOTAL 60 30 110 200 You would like to test his question of whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. Calculate a two variable chi-square test using an alpha (a) level of 0.01.

          This question has Z parts. Each of the 7 parts (Part A - Part G) has a dropdown list of possible answers. Choose the best answer from the dropdown list for EACH part of the question below.
A researcher is interested in whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. He classifies participants into three transportation groups (those who: bike/walk, take public transit or drive) and asks them how they typically feel on a normal Monday morning: happy/excited, angry/irritated, or sleepy. Data from his survey on 200 participants are presented below.
Happy/excited
Angry/irritated
Sleepy
TOTAL
Bike/walk
22
6
12
40
Public transit
18
6
36
60
Drive
20
18
62
100
TOTAL
60
30
110
200
You would like to test his question of whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. Calculate a two variable chi-square test using an alpha (a) level of 0.01.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jon Southam

09/21/2023

Step 1

- Expected counts under independence: E = (row total × column total) / 200 - Bike/Walk: Happy 12, Angry 6, Sleepy 22 - Public Transit: Happy 18, Angry 9, Sleepy 33 - Drive: Happy 30, Angry 15, Sleepy 55 - Observed counts (O) vs Expected (E) and (O−E)²/E: - Show more…

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This question has Z parts. Each of the 7 parts (Part A - Part G) has a dropdown list of possible answers. Choose the best answer from the dropdown list for EACH part of the question below. A researcher is interested in whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. He classifies participants into three transportation groups (those who: bike/walk, take public transit or drive) and asks them how they typically feel on a normal Monday morning: happy/excited, angry/irritated, or sleepy. Data from his survey on 200 participants are presented below. Happy/excited Angry/irritated Sleepy TOTAL Bike/walk 22 6 12 40 Public transit 18 6 36 60 Drive 20 18 62 100 TOTAL 60 30 110 200 You would like to test his question of whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. Calculate a two variable chi-square test using an alpha (a) level of 0.01.

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Transcript

00:01 So the question today is, is your desire to ride a bicycle dependent on your age? and so researchers asked 220 people randomly, 220 randomly selected people, and these four age ranges, whether or not they wanted to ride a bicycle, yes or no, and these are the counts.

00:19 And we're going to run a chi -squared test for independence to see if age matters in this context.

00:25 So the null hypothesis would be the two variables, age and interest in riding a bicycle are independent, so age does not affect the desire to ride a bike.

00:36 Or against the alternative, two variables are dependent, so age does affect.

00:41 And we're going to test this at the alpha of 0 .01 level of significance.

00:46 And let's go ahead and get our chi -squared statistic, which is found by taking the sum of the observed values, which we have, minus the expected values, which we'll get, divided by the expected values.

00:59 And that'll give us our chi -squared statistic.

01:01 Our expected values are the total in the row times the total in the column divided by the total in the table.

01:11 So these are the observed, i mean, to get the expected.

01:14 Here are the expecteds.

01:19 And so for example, to get this 26 .5, we take the total in the row, which is 55, times the total in the column, which is 106, and then we divide it by 220.

01:30 That's how we get 26 .5.

01:31 And just so happens, because there's 55 in each row, that the yeses are all the same, as are the nos, for the expected table.

01:39 So it's kind of interesting.

01:41 So now we're going to do the calculation, observe minus expected squared over expected, and this is what it's going to look like.

01:49 So this is the 17 to 24 yes, right here, observed minus expected squared over expected.

01:56 Then you do the nos, 18 over minus 28 .5 squared over 25, which is 28 .5.

02:04 Now we go down to the 25, 35, and then you go down the line.

02:09 That's the calculation.

02:11 As you can see, it's very repetitive.

02:12 That's why it's nice to have a computer do it for you...

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