# Essay on Exercises 2014 15 MAIN Topic 7 Chi Squa

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Topic 7 Exercises – Chi-Squared Tests

Answer questions with a total of 100 marks. Submit a written report (maximum 500 words) for the topic and Excel or SPSS files.

Where datasets from Anderson (2010) are mentioned these will be available on Moodle.

Use Excel or SPSS as appropriate

11. The file Lotto gives data on draws in the National Lottery for a 14 year period.
Column A shows draw number
Columns B-E shows the day of week and date
Columns F-K shows the six numbers drawn in order
Column L shows the machine used
Column M shows the set of balls.

Using appropriate Hypothesis Tests:

Assess whether there is evidence that some numbers are more or less likely to be drawn than others. Consider the 1st number drawn, the 2nd, the 3rd, the 4th, the 5th and 6th number drawn as well as all numbers irrespective of order.
10 Marks
Assess whether there is evidence of any dependence between numbers drawn and day of the week.
10 Marks
Assess whether there is evidence of any dependence between numbers drawn and machine used.
10 Marks
Assess whether there is evidence of any dependence between numbers drawn and the set of balls used.

10 Marks

12. The file Webpages gives the results of a survey to assess students’ views about a University’s web site.
Column A shows gender of respondent
Columns C-F shows whether they Agree or Disagree with the statements:
“Website is attractive to potential students”
“Website is easy to navigate”
“Website is up to date”
“I would refer the website to prospective students”

Using appropriate Hypothesis Tests:
For each of the four items C-F, test for the independence of the response and gender.
15 Marks
For each of the four items C-F, test for the independence of the response and level of study.
15 Marks
State an overall conclusion about the consistency of response for students of both genders and both levels of study.
10 Marks

13. The file Pharmaco shows employee aptitude scores for 50 randomly chosen job applicants. Using an appropriate chi-squared test (see example 4 in the notes) test the hypothesis that the population has a normal distribution.

Compare the result obtained with an alternative test for normality (the Shapiro-Wilk test) in SPSS:
Use Analyze-Descriptive Statistics-Explore
Move Score to Dependent List
Click Plots
Tick Normality tests with plots
Click Continue, Click OK.
The p-value is shown in the Tests or Normality output table under Shapiro-Wilk as Sig.

Note: Initially it may be useful to create a histogram of the data.
In SPSS use Graphs-Chart Builder and select histogram from the gallery tab.
In Excel explore the Histogram option in Data Analysis.
40 Marks

14. The SPSS file RealAle shows the results of a survey of beer drinkers categorized by the person’s gender and their favourite beer out of a choice of three.
(a) Using SPSS test the hypothesis that beer preference is independent of gender.
20 Marks

(b) Compare your result with the worked example in the Excel file Independence.
10 Marks

(c) Consider anything unusual about the data in the table of observed values, and investigate how it might influence the conclusion.
10 Marks

15. A survey of one thousand households with children is carried out. It includes questions on the number of children and whether at least one adult is working. The…