STAT1070 Statistics for the Sciences

（a）[尝试此问题的每个人都要求2分]使用SPSS，

（b）[尝试此问题的每个人都要求2分]假设我们有

（c）[尝试此问题的每个人都要求，满分6分]

（d）[尝试此问题的每个人都要求3分]
（c）部分中的分析假设？说明这些假设是否合理。
（e）[要求2-4人组成的小组尝试此问题，满分为2分]

（c）部分的答案中，要在此处获得分数，您需要写下一个公式，

（f）[尝试此问题的3-4人小组，要求2分]

（g）[每组4人，需要3分，这是必需的]

Question 2. [13-20 marks]
Only answer this question if you are not attempting Question 1 or Question
3.
According to the Australian census of 2016, the distribution of registered marital status
of Australians aged 15 years and over is shown below in Table 2:
Table 2: Distribution of registered marital status of Australians aged 15 years and over
from the 2016 census.
Marital status Proportion
Married 0.481
Separated 0.032
Divorced 0.085
Widowed 0.052
Never married 0.350
Suppose in 2020, a random sample of 200 Australians aged 15 years and over were asked
their registered marital status to see if these proportions have changed since the 2016
census. Their responses are shown in Table 3. The data are also contained in the file
marriage.sav.
Table 3: Counts from 2020 of the registered marital status for 200 randomly selected
Australians aged 15 years and over.
Marital status Count
Married 87
Separated 9
Divorced 15
Widowed 10
Never married 79
(a) [required for everyone attempting this question, 2 marks] Using SPSS,
construct a Pareto chart to visualise the distribution of registered marital status for
the sample of 200 Australians in Table 3. What does this chart suggest about the
distribution?
(b) [required for everyone attempting this question, 2 marks] Using the 2016
census data in Table 2, what is the probability that a person with a registered marital
status different from “married” has a registered marital staus of “never married”?
(c) [required for everyone attempting this question, 6 marks] Does the observed
data in Table 3 from the random sample of 200 provide evidence that the distribution
of registered marital status among Australians aged 15 years and over is different to

The University of Newcastle STAT1070 Statistics for the Sciences
the distribution from the 2016 census shown in Table 2? Be sure to state the null and
alternative hypotheses, the test statistic, the null distribution, the p-value, and an
appropriate conclusion in plain language. Use SPSS or Statstar to conduct the test,
(d) [required for everyone attempting this question, 3 marks] What are the
assumptions of the analysis you performed in part (c)? State whether these assumptions
are reasonable.
(e) [required for groups of 2-4 attempting this question, 2 marks] According
to the test you performed in part (c), what is the expected number of people with a
registered marital status of “never married” in the sample of 200? While the value
might be shown in the SPSS or Statstar output of your answer to part (c), to earn
marks here you need to write down a formula and derive the expected count.
(f) [required for groups of 3-4 attempting this question, 2 marks] Using the data
from the random sample of 200 Australians in Table 3, construct a 95% confidence
interval for the population proportion of Australians aged 15 years and over with a
registered marital status of “never married”. If you use SPSS or Statstar to answer
this question, provide all relevant output. If you derive the interval by hand, show all
steps. Write a sentence interpreting the interval in the context of marital status.
(g) [required for groups of 4 attempting this question, 3 marks] What are the
assumptions of the confidence interval you derived in part (f)? Are they reasonable?

The University of Newcastle STAT1070 Statistics for the Sciences
Question 3. [13-20 marks]
Only answer this question if you are not attempting Question 1 or Question
2.
Suppose the a random sample of 150 hospital patients were checked for type 1 diabetes
and hypertension. Table 4 gives the contingency table of the presence of these conditions
for each of the 150 patients. The data are also contained in the file diabetes.sav.
Table 4: Presence of diabetes and hypertension for 150 hospital patients.
Type 1 Diabetes
Positive Negative
Hypertension Hypertensive 18 31
Not hypertensive 13 88
(a) [required for everyone attempting this question, 2 marks] Using SPSS,
construct a stacked bar chart to visualise the relationship between the presence or
absence of type 1 diabetes and hypertension. What does this chart suggest about the
relationship?
(b) [required for everyone attempting this question, 2 marks] Suppose a patient
has hypertension. Using the data in Table 4, what is the probability that the patient
also has type 1 diabetes?
(c) [required for everyone attempting this question, 6 marks] Is there a statistically
significant association between whether or not a patient has type 1 diabetes and
whether or not the patient has hypertension? Be sure to state the null and alternative
hypotheses, the test statistic, the null distribution, the p-value, and an appropriate
conclusion in plain language. Use SPSS or Statstar to conduct the test, and provide
(d) [required for everyone attempting this question, 3 marks] What are the
assumptions of the analysis you performed in part (c)? State whether these assumptions
are reasonable.
(e) [required for groups of 2-4 attempting this question, 2 marks] Using the
data in Table 4, what is the expected number of patients who would have both type 1
diabetes and hypertension? While the value might be shown in the SPSS or Statstar
output of your answer to part (c), to earn marks here you need to write down a
formula and derive the expected count.
(f) [required for groups of 3-4 attempting this question, 2 marks] Using the
data from Table 4, construct a 95% confidence interval for the population proportion

The University of Newcastle STAT1070 Statistics for the Sciences
of patients with type 1 diabetes. If you use SPSS or Statstar to answer this question,
provide all relevant output. If you derive the interval by hand, show all steps. Write
a sentence interpreting the interval in the context of type 1 diabetes.
(g) [required for groups of 4 attempting this question, 3 marks] What are the
assumptions of the confidence interval in part (f)? Are they reasonable?

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