STATISTICS

Question 1

In a matched-pairs experiment, the statistical analysis is based on the differences between items within a pair.

(a) Give one advantage of setting up a matched-pairs experiment.

(b) What assumption is needed before the one-sample t-test can be applied to data collected from a matched-pairs experiment?

Question 2

Some employers use a framework of competencies to assess applicants for employment. The average score on the‚team working‚ competency was historically claimed to be 7.6. A particular employer wants to check the claim, so analyses the data from a randomly selected group of applicants who were assessed recently. The data are summarized as follows:

n = 17,

sample mean x = 8.39,

sample standard deviation s = 2.21.

(a) What are the number of degrees of freedom and the critical value for a t-test applied to these data?

(b) Calculate a 95% confidence interval for the population mean of the team working competency score using the critical value found in part (a).

Question 3

Education researchers believe that a new approach to tackling truancy may help to reduce truancy levels. They wish to carry out a trial to compare the efficacy of the new approach with an existing approach. It is known that some schools have lower truancy rates than others, and that schools have differing ways of dealing with truancy. Comment on how each of the following three designs may be applied to this trial, and clearly state any pros or cons for each.

(a) A group-comparative design

(b) A matched-pairs design

(c) A crossover design

Question 4

A university researcher conducts an experiment to see whether coaching would help to improve the parts of a competency score used to assess individuals for Registered Scientist status. A group-comparative design is used. Each group is asked to initially supply evidence to show how they meet five of the elements used in the score (shown below), chosen from the five core competencies used to assess Registered Scientist status. The evidence of each individual is then scored. Elements chosen to use in the experiment and for which evidence was requested:

A3: analyze, interpret and evaluate relevant scientific information, concepts and ideas, and propose solutions to problems.

B3: promote and ensure the application of quality standards.

C1: demonstrate effective and appropriate communication skills.

D4: contribute to continuous performance improvement.

E1: comply with relevant codes of conduct and practice.

One group of 20 applicants then receives a set of web links and two interactive coach-led sessions via the web on the type of evidence to supply. Two weeks later they are asked to resubmit their evidence. The second group comprises a different group of 20 who were just given the set of web links and then asked to resubmit their evidence two weeks later. The change in the score for each individual is recorded. The resulting data are to be analyzed using a hypothesis test.

(a) What type of data are produced in this experiment?

(b) From the hypothesis tests listed,

give the most appropriate test for analyzing these data, together with two reasons for your answer.

(c) XXX has added to your skills in the five elements above that are used to assess Registered Scientist status. Choose three of the areas, and give one specific example for each area chosen of how your skills have improved

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