Foundations Of Statistics Work Integrated Learning Report

The Industry Scenario

You are a new graduate researcher at the Amberly Mental Health Service. You have been given a dataset of Queensland Mental Health Service clients to analyse. These clients attended an intervention program designed to improve the participant's avoidance coping strategies. Extent of avoidance coping was recorded at the beginning and end of the intervention program, with external aggression and internal aggression [hostility] also recorded at the end of the intervention program. Demographic data was also collected for each client, regarding their gender and birth order. You have been tasked with conducting the initial analysis of some variables using SPSS and to write brief reports.

Assignment

For your Assignment,you are required to complete the first three [3] questions by producing the appropriate analyses and writing the relevant report for each question. You are also required to complete questions 4 and 5, which contain short answer questions.

For each of the first three questions requiring SPSS, you should include the relevant output [eg tables and graphs] with your report. Note that some of the variables have similar names, so it is important that the correct variable be selected to address the question asked.

Question 1: Birth Order

The variable Birth indicates the birth order of each client. Using SPSS, summarise the Birth variable and write a paragraph explaining the key features of the data observed in the output in the style presented in Supplement B: Reporting information about single variables.

Question 2: Height

The variable Height measures the height in cm for each client. Using SPSS, summarise the Height variable and write a paragraph explaining the key features of the data observed in the output in the style presented in Supplement B: Reporting information about single variables.

Question 3: Internal Aggression

The variable AggInt measurs the internal aggression [hostility] of each client. This variable was scored on a scale from 0 to 20, with higher scores representing greater levels of internal aggression [hostility]. Using SPSS, produce the relevant output to summarise the AggInt variable and write a paragraph explaining the key features of the data observed in the output in the style presented in Supplement B: Reporting information about single variables.

Question 4: [does not require SPSS]

Susan is an engineering student who decides to take part in three competitions where puzzles need to be solved as quickly as possible by correctly fitting all the pieces of a gadget together in each case. In Competition A, she takes 125 seconds to complete the puzzle, in Competition B she takes 140 seconds, and in Competition C she takes 118 seconds. Overall completion times for participants in Competition A are normally distributed with a mean of m = 119 seconds and a standard deviation s = 7 seconds. Completion times for participants in Competition B are normally distributed with a mean of m = 165 seconds and a standard deviation s = 15 seconds.

Completion times for participants in Competition C are normally distributed with a mean of m = 109 seconds and a standard deviation s = 8 seconds. In which competition was Susan's performance better, relative to others who took part in that competition? Justify your answer, quoting relevant statistics as part of your explanation.

Question 5: [Does not require SPSS. No calculations are required]

The Betterbuy Battery Company manufactures alkaline and lithium batteries for use in torches, radios and other similar devices. They claim that the average operating time of their alkaline batteries is 20.00 hours, with a standard deviation of 1.50 hours. However, a consumer organisation believes the average operating time of their alkaline batteries is lower than 20.00 hours.

In order to investigate this further, the consumer organisation take a random sample of 625 alkaline batteries manufactured by the company during March and tests each battery by putting it in a torch and recording the number of hours it operates for.

1. What is the population we can draw conclusions about inthis study?

To answer questions (b) to (d), consider only the sampling distribution shown in Figure 1.

: Distribution of sample means in 300 samples of size 625, taken from a population where the mean is 20.00 hours and the standard deviation is 1.50 hours.

1. > does the highlighted section of the distribution in Figure 1 represent?
2. The random sample of 625 batteries taken by the consumer organisation turned out to have a mean operating time of 20.16 hours. Does this sample look like it belongs to the sampling distribution displayed in Figure 1? Justify your answer.
3. Given that the sample was randomly selected from all batteries manufactured by the Betterbuy Battery Company in March, and given that each battery's operating time was measured accurately, what conclusion can we reach from part (c)?

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