Question 180480: The data in the table that follows was collected by a large car manufacturer concerning a new prototype car called the CIELO. Thirty carefully selected respondents were shown the car and fully briefed about its capabilities. Here is the data, which includes age (intervally scaled), sex (nominal), social status (interval scale ranging from 10, low status, to 30, high status), attitude toward CIELO (interval scale ranging from 6, negative attitude, to 30, positive attitude) and intention to purchase CIELO (nominal, yes or no).
Is there any difference in male and female attitude scores toward the CIELO? Is there anything unusual about this data? Please note that we have to setup a hypothesis test of the difference in two population (female respondents and male respondents) means (attitude scores).
RESPONDENT #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
AGE
20
19
34
23
42
55
24
26
35
41
43
51
56
62
43
51
28
19
24
26
28
35
38
23
42
41
30
29
19
26
SEX
M
F
M
M
M
F
F
M
F
M
F
M
M
F
F
F
M
M
M
F
F
M
F
M
F
F
F
M
M
F
SOCIAL STATUS
15.6
17.5
28.2
24.6
16.5
12.2
12.5
29.6
27.6
23.2
21.2
20.2
19.4
18.6
10.2
14.3
12.6
14.8
29.6
26.5
23.2
17.9
19.9
20.1
18.6
18.6
24.6
26.6
14.5
12.9
ATTITUDE SCORE
16
15
14
6
28
24
19
14
23
16
26
28
14
12
11
10
22
24
19
18
20
23
23
25
17
17
16
13
22
21
INTENTION TO PURCHASE
Y
Y
N
N
Y
N
Y
N
N
N
Y
N
N
Y
Y
N
Y
N
N
Y
N
N
N
Y
N
N
Y
N
Y
N
My question: Am I on the right track and/or if not can you please show me how to set up the hypothesis test and solve for it?
I got this:
Female: 272/15 = 18.133
Male: 284/15 = 18.933
H0: (Mu) less than or equal to 18
H1: (Mu) greater than 18
Small Sample
18.133 – 18.933/Sqrt 30(squared)*(1 over 15 + 1 over 15) = (0.8) / 900 * 2 over 15 = 120
(-0.8)/Sqrt 120 = (-0.8) / 10.954 = 0.073
Large Sample
18.133 – 18.933/Sqrt 30(squared) / 30(squared)over 15 / 30 (squared) over 15
= (0.8)/900 over 15 + 900 over 15
= (0.8)/ 60+60 = (0.8) / 120 = 0.006
Q: I am not sure if these are the right samples to use or if I should use a paired “t” sample? (below)
15
30 / sqrt (?)
Thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! My question: Am I on the right track and/or if not can you please show me how to set up the hypothesis test and solve for it?
I got this:
Female: 272/15 = 18.133
Male: 284/15 = 18.933
-------
Comment: I'm going to assume your mean calculations are correct.
-----------------------------------------------------------------
You need a 2-Sample Z-test addessing the question of difference between
the attitude of the sexes.
---------------------------------------------------------
H0: u(men)-u(women) = 0
H1: u(men)-u(women) is not 0
---------------------------------
Assuming alpha = 5% the Rule for the 2-Sample test is "Reject Ho if
test statistic is Less than -1.96 or greater than +1.96.
----------------------------------------------------------
Small Sample
Test statistic: (18.133 – 18.933)/Sqrt [30(squared)*(1 over 15 + 1 over 15) = (0.8) / 900 * 2 over 15 = 120
(-0.8)/Sqrt 120 = (-0.8) / 10.954 = 0.073
---
Comment: I can't follow you here:
I got the following:
t.s. = (difference of sample means)/sqrt[(s(men))^2/15 + (s(women))^2/15]
I ran it on a TI-calculator and got z = -0.073..
-----------
If that is right, since t.s. is not in the reject interval, Fail to reject
Ho. There is no statistical difference in attitude toward CIELO by the
sexes.
Large Sample
18.133 – 18.933/Sqrt 30(squared) / 30(squared)over 15 / 30 (squared) over 15
= (0.8)/900 over 15 + 900 over 15
= (0.8)/ 60+60 = (0.8) / 120 = 0.006
Q: I am not sure if these are the right samples to use or if I should use a paired “t” sample? (below)
Whether you use "t" or "z" depends on your textbook requirements or your
professor's directions. By the way, what is the textbook and what is the
chapter and problem number?
==============================
Comment: I would appreciate your feedback on these comments. Do they
help? Are they confusing or contradictory?
====================================
Cheers,
Stan H.
15
30 / sqrt (?)
Thank you
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