STATISTICS MULTIPLE CHOICE

Multiple choice:

1. To halve the margin of error of an opinion poll in general it is necessary to [1 mark]
2. Halve the sample size
3. Double the sample size
4. Triple the sample size
5. Quadruple the sample size

2. Which of the following divides a sample into two equal parts? [1 mark]
3. Mean
4. Median
5. Standard deviation
6. 2 x standard deviation

3. A list of 5 pulse rates is: 70, 64, 80, 74, 92. What is the median for this list? [1 mark]
4. 74
5. 76
6. 77
7. 80

The following questions (4 and 5) refer to the contingency table below which classifies students by age and sex

AGE (years) male             female

≤ 25               120 30

> 25               20                    40

4. What is the marginal relative frequency of males? [1 mark]
5. 3/5
6. 4/7
7. 2/3
8. None of the above

5. What is the conditional relative frequency of those aged over 25, given that they are female? [1 mark]
6. 2/7
7. 3/7
8. 4/7
9. None of the above

6. If the correlation between the number of cigarettes smoked in a lifetime and the incidence of cancer is 0.35, then [1 mark]
7. Smoking causes cancer
8. Cancer causes smoking
9. There is a third factor that caused both smoking and cancer
10. No conclusion can be drawn
11. What is the correlation coefficient for the three pairs of numbers x and y?

x              -2            0             4

y              1              0              -2

1. -1
2. 0
3. 1
4. None of the above

8. The p-value obtained from a two tailed test of a null hypothesis that a parameter value is zero against an alternative hypothesis that the parameter is larger than zero is the probability that [1 mark]
9. The null hypothesis is true
10. The observed value of the test statistic will occur if the null hypothesis is true
11. The observed value of the test statistic is statistically significant
12. Any value as large as or larger than the test statistic will occur if the null hypothesis is true

9. Which of the following statistical test is applicable for one sample from a skewed distribution? [1 mark]
10. Z-test
11. Student’s t-test
12. Chi-square test
13. Correlation test

10. A contingency table has 6 rows and 3 columns. So the degrees of freedom for a test of the hypothesis that the two variables are independent is [1 mark]
11. 2
12. 18
13. 17
14. 10

11. A distinction between a population parameter and a sample statistic is:

[1 mark]

1. A population parameter is only based on conceptual measurements, but a sample statistic is based on actual measurements.
2. A sample statistic changes each time you try to measure it, but a population parameter remains fixed.
3. A population parameter changes each time you try to measure it, but a sample statistic remains fixed across samples.
4. The true value of a sample statistic can never be known but the true value of a population parameter can be known.

12. A survey asked people how often they exceed speed limits. The data were then categorized into the following contingency table of counts showing the relationship between age group and response. [1 mark]

Exceed speed limit

AGE (years)    sometimes     never

≤ 30                        100                100

> 30                        40                  260

What is the relative risk of exceeding the speed limit for people under 30 compared to people over 30?

3. 3.75
4. 0.4
5. 0.27
6. 40%

13. A chi-square test involves a set of counts called “expected counts.” What are the expected counts? [1 mark]
14. Hypothetical counts that would occur if the alternative hypothesis were true.
15. Hypothetical counts that would occur if the null hypothesis were true.
16. Hypothetical counts assuming all categories are equally likely.
17. The counts over a long time that would be expected if the observed counts are representative.

14. A pharmaceutical company claims that its antihypertensive drug allows people to reduce their blood pressure by 8mm of mercury after one month of treatment. If we want to conduct an experiment to determine if the patients‟ blood pressure is not being reduced to the level advertised, which of the following hypotheses should be used?[1 mark]
15. H0: μ = 8; Ha: μ > 8
16. H0: μ = 8; Ha: μ ≠ 8
17. H0: μ = 8; Ha: μ < 8
18. H0: μ ≠ 8; Ha: μ < 8

15. simple random sample of size n = 25 is drawn from a population with mean 50 and standard deviation 5. What is the standard deviation of the sample mean x ?

[1 mark]

1. 1
2. 2
3. 5
4. 10

SHORT ANSWER QUESTIONS

1. You’ve just been appointed to work as a Health Promotion Officer in Longreach, central Queensland. The management of diabetes is a critical local health issue. An advanced medical clinic was recently set up in the centre of town, but those most in need, particular non-town residents, do not appear to be using it. You think access might be a critical barrier. You’ve read a recent evaluation report about a mobile service operating in a similar area that involves a multidisciplinary team travelling to patients in remote locations.

Your supervisor thinks this might be a good option, but she wants evidence that the community would use such a service. She asks you to conduct a survey, but you suggest that before you do that you should examine community perceptions in more detail. You suggest a qualitative study would be a good place to start.

1. Briefly identify one reason to justify your proposal to conduct a qualitative study? [1 mark]
2. Identify two methods you could use to collect data on this issue. [2 marks]
3. What sample strategy will you use to identify people for your study? Provide an explanation of the sample strategy you have chosen and briefly justify why you have chosen it. [2 marks]

2. To determine whether the mean nicotine content of a brand of cigarettes is greater than the advertised value of 1.4 milligrams, a health advocacy group tests the null hypothesis H0 : µ = 1.4 against the alternative hypothesis Ha : µ > 1.4

The sample of 100 cigarettes had a mean of 1.2 milligrams and the population standard deviation was known to be 0.8. A z-test statistic was calculated.

1. Explain why a z-test statistic was used instead of a t-test statistic. [1 mark]
2. Calculate the standard error of the sample mean. [1 mark]
3. Calculate the z-test statistic. [1 mark]
4. The p-value derived was 0.006. Is this significant at the 1% level? [1 mark]
5. Explain the result of the test in words to someone who knows no statistics

[1 mark]

3. An opinion poll company asked a random sample of 1009 adults which causes of death they thought would become more common in the future. Topping the list was car accidents: 70% of the sample thought deaths from car accidents would increase.
4. How many of the 1009 people interviewed thought deaths from car accidents would increase? [1 mark]
5. The margin of error for this poll is reported to be plus or minus 3 percentage points. Explain to someone who knows no statistics what “margin of error plus or minus 3 percentage points” means. [1 mark]
6. Give a 95% confidence interval for the proportion of people who think deaths from car accidents will become more common. [1 mark]
7. Explain what this confidence interval means. [1 mark]
8. Compare your confidence interval with the margin of error of 3 percentage points reported by the company – why or why not do they differ? [1 mark]

4. The Abstract below is from the following paper:

Law, C.-k., Sveticic, J. and De Leo, D. (2014), Restricting access to a suicide hotspot does not shift the problem to another location. An experiment of two river bridges in Brisbane, Australia. Australian  nd New Zealand Journal of Public Health, 38: 134–138.

Background: Restricting access to lethal means is a well-established strategy for suicide prevention. However, the hypothesis of subsequent method substitution remains difficult to verify. In the case of jumping from high places („hotspots‟), most studies have been unable to control for a potential shift in suicide locations. This investigation aims to evaluate the short- and long-term effect of safety barriers on Brisbane’s Gateway Bridge and to examine whether there was substitution of suicide location.

Methods: Data on suicide by jumping – between 1990 and 2012, in Brisbane, Australia – were obtained from the Queensland Suicide Register. The effects of barrier installation at the Gateway Bridge were assessed through a natural experiment setting. Descriptive and Poisson regression analyses were used.

Results: Of the 277 suicides by jumping in Brisbane that were identified, almost half (n=126) occurred from the Gateway or Story Bridges. After the installation of barriers on the Gateway Bridge, in 1993, the number of suicides from this site dropped 53.0% in the period 1994–1997 (p=0.041) and a further reduction was found in subsequent years. Analyses confirmed that there was no evidence of displacement to a neighbouring suicide hotspot (Story Bridge) or other locations.

Conclusions: The safety barriers were effective in preventing suicide

A summary of Table 1 is as follows.

Suicides by jumping from a high place in Brisbane: 1990-2012

Gateway       Story     Other bridges    Other jumping sites       Total

1990-1993            22         15                             6                              13                           56

1994-1997            11         17                       2                           16                    46

1998-2012              5         56                     12                          102                      175

Total                       38       88                      20                        131                       277

Answer the following questions, briefly justifying your answer.

1. What is the study design? [2 marks]
2. For the comparison of suicide numbers from the Gateway bridge between the periods 1990-93 and 1994-97.
3. State the null hypothesis and alternative hypothesis being tested.

[1 mark]

ii Explain how the hypotheses would be tested (the actual calculations are not needed). [2 marks]

1. How would you test the hypothesis that the proportions of suicides from the four different locations did not change over the three time periods (the actual calculations are not needed)? [3 marks]
2. Is the conclusion in the Abstract justified by the results? [2 marks]