Calculating 95% and 99% confidence intervals and testing a hypothesis.
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2 Questions: 3) Using the CIELO data, calculate 95% and 99% confidence intervals for the percentage intending to purchase the CIELO.
(see attachment for full question)
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3) Using the CIELO data, calculate 95% and 99% confidence intervals for the
Percentage intending to purchase the CIELO
4) Test the hypothesis that more one-third of the general driving population would
be willing to purchase the CIELO
To solve problem 3 & 4 use the table below.
The in the table below was collected by a large car manufacturer concerning a new prototype car called CIELO. Thirty carefully selected respondents were shown the car and carefully briefed about its capabilities.
Here is the data which include age (intervally scaled), sex (nominal), social status (interval scale ranging from 10, low status to 30, high status), attitude toward CIELO (interval scale from 6, negative to attitude to 30, positive attitude) and the intention to purchase CIELO (nominal, yes or no).
A - Is there any difference in male and female attitude toward CIELO?
B - What is the relationship between intention to purchase and gender?
C- Is there anything unusual about this data?
Social Attitude intention
Respondent Age Sex Status Score to purchase
1 20 M 15.6 16 Y
2 19 F 17.5 17.5 Y
3 34 M 28.2 14 N
4 23 M 24.6 6 N
5 42 M 16.5 28 N
6 55 F 12.2 24 N
7 24 F 12.5 19 Y
8 26 M 29.6 14 N
9 35 F 27.6 23 N
10 41 M 23.2 16 N
11 43 F 21.2 26 Y
12 51 M 20.2 28 N
13 56 M 19.4 14 N
14 62 F 18.6 12 Y
15 43 F 10.2 11 Y
16 51 F 14.3 10 N
17 28 M 12.6 22 Y
18 19 M 14.8 24 N
19 24 M 29.6 19 N
20 26 F 26.5 18 Y
21 28 F 23.2 20 N
22 35 M 17.9 23 N
23 38 F 19.9 23 N
24 23 M 20.1 25 Y
25 42 F 18.6 17 N
26 41 F 18.6 17 N
27 30 F 24.6 16 Y
28 29 M 26.6 13 N
29 19 M 14.5 22 Y
30 26 F 12.9 21 N
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Solution Summary
The question outlines the process of computing confidence intervals and testing a hypothesis. Formulas and process are discussed and calculations are provided in Excel.
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3) First, we translate the variable X="intension to purchase" into numeric form:
X=1 if "Yes" ; X=0 if "No"
Then we calculate the expected percentage of purchasing intension, which is the mean of X. i.e. Xm=0.367 (the calculation can be referred to the attached EXCEL file)
The standard deviation of X is Sd=SQRT((X-Xm)^2/(n-1))=0.490
So the standard error is ...
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