BSB110 - Data Analysis for Management – PRACTICE Test 1 – Chi-Squared


In your answers to each numeric question please give your answer correct to TWO Decimal Places, except where

a) an integer is clearly expected, and

b) where the question asks for something different.

Something different is indicated by, say, 5 d.p. meaning 5 decimal places.



If you are asked to enter some integer numbers , such as 3,6,11 & 13 as a set , you must enter {3,6,11,13}

– the curly brackets & commas are crucial.

You will need a table of critical values for the Chi-Squared distribution and throughout your tests you should use the 5% level of significance.





Town Centre Planning

The town council of “Much Kastels” (MK) is considering changes to their town centre along the lines made to the nearby town of “Rite Manors” (RM). Some people have praised the recent changes in RM but others have suggested they only appeal to female visitors, so the MK councillors have commissioned a survey of people in the new RM town centre on several weekends. The respondents were asked to rate the attractiveness of the RM town centre changes on a scale of 1 to 7, where 1 means extremely unattractive and 7 means extremely attractive. The respondents were also asked to identify their gender, but a few respondents declined to give that information.

The responses have been summarised and are shown in the table below and the councillors wish to test if there is any link between the gender of the respondents and their attraction to the RM changes.



Gender Identified
Attractiveness
Rating Female Male Not Given
1 1 0 1
2 1 3 0
3 2 5 0
4 36 52 0
5 120 80 1
6 71 18 0
7 9 2 0
Total 240 160 2
I
The null hypothesis in this case is that the variables "Gender" and "Attractiveness of the RM change" are
not linked/independent


Assuming the null hypothesis and using all the data as given in the table:
What is the expected number of respondents with an attractiveness rating of 1 who have Not Given their gender ?(5 d.p)
What is the Chi-Squared value in the cell for those with an attractiveness rating of 1 who have Not Given their gender? (5 d.p)
What is the expected number of Female respondents with an attractiveness rating of 4 ?
What is the expected number of Male respondents with an attractiveness rating of 7?



Before doing a valid Chi-squared test you may need to take some appropriate action.

At the outset do you need to remove any rows?
(No answer given)

At the outset do you need to remove any columns?
(No answer given)

After removing any rows or columns to do you need to recalculate the expected values?
(No answer given)
.




Now remove the necessary column and recalculate the expected values.

What is now expected number of female respondents, with attractiveness an rating of 3?

What is expected number of male respondents, with an attractiveness rating of 7?

Which ratings rows have at least one expected value less than 5? Enter,(as a set) up to 5 ratings values or {0} if none,

Which ratings rows have at least one expected value greater than 150? Enter, (as a set) up to 5 ratings values or {0} if none,


Before doing a valid Chi-squared test you may need to take some further appropriate action.

Your appropriate action involved:

Removing how many rows?
Merging how many rows?

After taking appropriate action, your data table now has:
How many rows?
How many columns?
How many degrees of freedom?
For your data now, what is the critical value of Chi-Squared at the 5% level?
What is now the expected number of Male respondents, with an attractiveness rating of 4 ?

What is Chi-Squared value in cell for Male respondents, with attractiveness rating 4 ?


What is now the overall Chi-Squared value of your table?
What is the conclusion about the null hypothesis?
(No answer given)

In conclusion, the variables "Gender" and "Attractiveness of the RM changes" are?
(No answer given)
What comments would you make? Enter, as a set, one or two or three numbers of your chosen comments from the list below ( enter your numbers using curly brackets and commas. eg {1} or {1,2}).


Number Comment
1 None
2 Great
3 As expected
4 That’s not expected
5 Valid
6 Not valid
7 Need more data
8 Too many big values
9 Too many small expected values
10 Large expected values
11 Expected value under 5
12 Overall, the RM changes are attractive to most people
13 Males are more attracted by the RM changes
14 Females are more attracted by the RM changess
15 No significant difference in RM changes attractiveness based on gender