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STA10003 FOUNDATIONS OF STATISTICS ASSIGNMENT - P

Semester / Study Period: Study Period 1 Year: 2020 Unit code: STA10003 Unit name: Foundations of statistics Assignment Number: Part 1 worth 20% of your final mark for STA10003 Your name: Student number: Date submitted: Please retain a hard copy of your assignment as you will be required to resubmit it if requested

Instructions Type your answers in the spaces provided in this document

Submission Instructions 1. Your submission must be a single Word file or PDF file. 2. An answer template is provided, and is recommended for use. You may need to resize your output to fit. 3. A cover page is not required, though you should include your name and student number within the document 4. You must submit your file via Canvas by the specified due date and time. 5. Once submitted, please review your submission to ensure the correct file has been submitted. 6. Only the last document you submit will be marked. 7. This is an individual assignment. Do not share your work with other students. They will have a different random sample of data, so any copying will be detected.

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Question 1 The variable PsychDistress_Cat indicates the psychological distress category of each of the Californian adults. Using SPSS, summarise the PsychDistress_Cat 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.

The distribution of Psychological Distress for a sample of 1283 Californian adults is displayed in Figure 1. As shown, the distribution is roughly symmetric and unimodal. There doesn’t appear to be any outliers. The average Psychological Distress in Californian adults is 1.08, and the standard deviation is .801. Majority of adults reported to have low psychological distress (55.5%). Although, adults with no distress (21.5%) and moderate distress (16.2%) were relatively low. Adults with high distress (6.8%) reported to have the lowest percentage of the 1283 adults. Include your SPSS output for this question here

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Question 2 The variable Weight gives an indication of the weight (kg) of the adults. Using SPSS, summarise the Weight 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.

The distribution of the weight [kg] of Californian adults for a sample of 1246 people is displayed in Figure 1. The distribution is positively skewed, with the average weight of adults being 77.98 kg, standard error .54952 kg. Typically, the average weight [kg] of Californian adults was between 63.5kg and 88.9kg, with 50% of the adult’s weight falling within this range. One respondent reported weighing significantly more than other adults, with the maximum weight of 150kg.

Include your SPSS output for this question here

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Question 3 The variable PsychDistressScore gives an indication of the psychological distress score for each participant on the Kessler K6. Using SPSS, produce the relevant output to summarise the PsychDistressScore 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.

The distribution of the Psychological Distress scores [Kessler K6] in a random sample of 1228 respondents is displayed in Figure 1. The distribution is positively skewed, with 50% of respondents having an average Psychological Distress Score of 3.58, standard error .113. Typically, Psychological Distress Scores were between 1.00 and 5.00, with half of the scores falling within this range. It is reported that some respondents had exceptionally high scores of Psychological Distress, of over 18, with the highest being 24 on the Kessler K6. Include your SPSS output for this question here

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Question 4 [does not require SPSS] Cheryl enjoys competing in amateur triathlons. She wants to improve her swimming and cycling times. To improve her race times Cheryl enters a swimming event and a bike event. In the swimming event, Cheryl takes 59 minutes to complete the 3.9km course. In the bike race Cheryl takes 289 minutes to complete 180km. Overall completion times for participants in swimming event are normally distributed with a mean of  = 70 minutes and a standard deviation  = 6 minutes. Completion times for participants in the bike event are normally distributed with a mean  = 300 minutes and a standard deviation  = 9 minutes. In which competition was Cheryl’s performance better, relative to others who took part in that competition? Justify your answer, quoting relevant statistics as part of your explanation.

To determine the competition in which Cheryl’s performance was better, the z-score formula must be used. That is, the score minus the mean, divided by the standard deviation.

According to the formula, Cheryl’s performance time in the swim event, corresponds to a z-score of -1.83. This indicates a z-score that is below the mean by almost -2 standard deviations. Conversely, in the bike event, Cheryl’s performance time has a z-score of -1.22. That is, the score is located -1.22 standard deviations below the mean.

The score which is closest to the mean was the bike event, with a z-score of -1.22. Therefore, Cheryl’s overall performance and race time was better in the bike event.

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Question 5 [does not require SPSS] Taronga Zoo is one of the top-rated tourist attractions in Sydney. In 2018, 42% of all visitors at the Taronga Zoo were from overseas. As the number of tourists increases every year, the management of the zoo predicted that a higher proportion of overseas tourists would visit the zoo in 2019. To test this prediction, the researchers randomly select 1000 people who visited the zoo in March 2019. a. What is the population we can draw conclusions about in this study?

The researcher randomly selects 1000 people who visited the zoo in March 2019. In this instance, the population is 1000. To answer questions (b) to (d), consider the sampling distribution shown in Figure 1.

Figure 1. Distribution of sample proportions in 300 samples of size 1000, taken from a population where the proportion is 0.42 b. What does the highlighted section of the distribution in Figure 1 represent?

The highlighted section of the distribution represents the frequency (number of samples). 15 out 300 samples have a proportion of tourists from overseas =0.395 c. The random sample of 1000 visitors turned out to have a proportion of 0.44. Does this sample look like it belongs to the sampling distribution displayed in Figure 1? Justify your answer.

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It can be assumed that the distribution shown in Figure.1 is normally distributed and symmetric about the proportion 0.42. The position of the sample proportion 0.42 falls within 1.96 standard deviations of the mean which can be seen in Figure 1 at a 5% significance level. Therefore, no evidence suggests this sample belongs to a different population.

d. Given that the sample selection was unbiased, and that the origin of the visitors was accurately recorded, what conclusion can we reach from part (c)?

The random sample of visitors with the proportion of 0.44 looks like it belongs the same population with a proportion of 0.42. This indicates that the difference between the two is insignificant. Therefore, there is sufficient evidence to conclude that the prediction a higher proportion of tourist would visit Taronga Zoo in 2019 may be incorrect.

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