STA10003 FOUNDATIONS OF STATISTICS WORK INTEGRATED LEARNING (WIL) ASSIGNMENT

ASSIGNMENT – PART 1

For your Assignment - Part 1 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 is selected to address the question asked.

 Question 1: Political orientation on social issues

 The variable Q22_r1 indicates the political orientation on social issues for each respondent. Using SPSS, summarise the Q22_r1 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: Age

 The variable Q14 measures the age in years for each respondent. Using SPSS, summarise the Q14 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: Imagination Facet

 The variable Q1_IF measures the imagination facet for each respondent. This variable is scored on a scale from 1 to 4 with higher scores representing greater levels of imagination. Using SPSS, produce the relevant output to summarise the Q1_IF 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]

 Imogen likes to enter competitions in which puzzles need to be solved as quickly as possible by correctly fitting all the pieces of a gadget together. In Competition A Imogen takes 263 seconds to complete the puzzle, in Competition B they take 231seconds, in Competition C Imogen takes 298 seconds to complete the puzzle, and in Competition D they take 226 seconds. Overall completion times for participants in Competition A are normally distributed with a mean ? = 240 seconds and a standard deviation s = 24 seconds. Completion times for participants in Competition B are normally distributed with a mean ? = 262 seconds and a standard deviation s = 27 seconds.

Completion times for participants in Competition C are normally distributed with a mean ? = 261 seconds and a standard deviation s = 32 seconds. Completion times for participants in Competition D are normally distributed with a mean ? = 271 seconds and a standard deviation s = 40 seconds. In which competition was Imogen’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 current Impressionist exhibition at The Lume in Melbourne is a very popular attraction. People from all over Australia, and from overseas have been visiting. The previous exhibition at The Lume was a Van Gogh exhibition and 15% of all visitors to the Van Gogh exhibition were from overseas. As the number of tourists coming to Melbourne has increased the management of The Lume predicted that a higher proportion of overseas visitors will come to the Impressionist exhibition than came to the Van Gogh exhibition. To test this prediction a random sample of 850 visitors who came to the Impressionist exhibition at The Lume in February 2023 was taken. 

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

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

No calculations are required.

 .118 .126 .134 .142 .150 .158 .166 .174 .182

Figure 1. Distribution of sample proportions in 300 samples of size 850 taken from a population where the proportion is 0.150 

1. Whatdoes the highlighted section of the distribution in Figure 1 represent?
2. In the random sample of 850 it was found that 17.6% of visitors were fromoverseas, a proportion of 0.176. Does this sample look like it belongs to the sampling distribution displayed in Figure 1? Justify your 
3. Using this random sample of 850 visitors what conclusion can you makeabout the prediction made by the management of The Lume? Make use of the sampling distribution and your answer in part c.

How to generate your random sample of 1500 observations.

1. Open the STA10003 Sem 1 2023 Assignment Data.sav data file. From the Transform drop-down menu, select Random Number Generators from the menu 

2. From the Random Number Generators dialogue box, click the boxes beside SetActive Generator and Set Starting Point as shown below. Then click  

3. From theData drop-down menu, choose Select Cases 

4. From the Select Cases dialogue box, choose Random Sample of Cases and then click theSample button [the Sample button is pale blue with greyscale font until you select the Random sample of cases choice]: 

5. From the Select Cases: Random sample dialogue box, click Exactly and type 1500 cases fromthe first 2980. Again the information is pale blue until you select ‘Exactly’. We want to generate a random sample of 1500 from the entire data set, so enter 1500 cases from the first 2930 

 After entering the information above, click Continue [this returns you to the Select Cases Dialogue Box where you will see, next to the Sample button, confirmation of the 1500 cases selected]. 

6. Wecan remove the unselected cases by clicking the Delete unselected cases button under the Output heading. 

7. Afterclicking OK, your data set will now only show the 1500 cases 
8. Youshould now save the data file with a new name.

The data file is ready to use for your Assignment!

Note: Your data file containing a random sample of 1500 cases will also be used in Assignment Part 2, so ensure that you save it in a ‘safe’ place.