Assignment 2: Inferential Statistics

|Hand out: |Week 7 | |Hand in : |Week 11 |

1. [8 marks]

What are parameters and statistics (or estimates)? List two of the parameters and their corresponding statistics that were covered in Topics 7 & 8, and give examples of each.

2. [4 × 8 = 32 marks]

Identify each of the following studies as a survey, observational study, or experiment; and list the descriptive (numerical & graphical) and inferential tools that you would use to analyse the data. [Hint: Use the summary tables at the end of your Topic 2, 3, and 7 lecture notes to choose descriptive and inferential tools.] To gain full marks you must explain your choices.

a) A random sample of 50 households was selected from a list of households in each of Albury and Wodonga (i.e., 100 households in total were selected), and each household was visited to determine whether they have a rainwater tank (yes or no). The question of interest is whether there is evidence of a difference between the proportions of households with rainwater tanks between the two towns.

b) Can pleasant aromas help a student learn better? There is reason to believe that the presence of a floral scent can improve a person's learning ability in certain situations. To test this hypothesis, 50 people were randomly assigned to one of two treatment groups. One group worked through a set of pencil and paper mazes while wearing a floral-scented mask. The other group performed the same tasks while wearing an unscented mask. Testers measured the length of time it took subjects to complete each of the trials.

c) To determine whether hormone-replacement therapy (HRT) increases the risk of breast cancer, a sample of 100 volunteers was randomly divided into two groups, one receiving HRT and one receiving a placebo (i.e., a sugar tablet containing no hormone). After a period of two years each subject was followed up to determine whether or not they had contracted breast cancer.

d) To determine whether Australian Workplace Agreements (AWAs) increase productivity, a sample of 50 medium-sized retail businesses that employ workers on individual contracts (i.e., AWAs) was compared with a sample of 50 medium-sized retail businesses that employ workers on collective bargaining agreements. The productivity of each business was measured in terms of the sales (in dollars) made per employee over the last 12 months.

3. [10 marks]

You randomly choose 10 rental properties (unfurnished one-bedroom apartments) in each of Wodonga West and Wodonga East from a large list of such properties that were advertised in the local newspaper. You calculate the mean and standard deviation of the advertised rental prices as shown in the table below. Is there evidence of a difference in mean (weekly) rental price between the two suburbs? To gain full marks you must state the parameter of interest and hypotheses, choose an appropriate test statistic, compute the p-value and confidence interval, and write your conclusion. [Note that a dot plot gave no reason to suspect the data were nonnormal.]

|Suburb |Mean |Standard deviation |Sample size | |Wodonga West |$105 per week |$5 per week |10 | |Wodonga East |$100 per week |$6 per week |10 |

4. [10 marks]

In the United States approximately 900 people die in bicycle accidents each year. One study examined the records of 1711 bicyclists aged 15 or older who were fatally injured in bicycle accidents between 1987 and 1991 and were tested for alcohol. The following...