Question 16 [4 marks]

A researcher for a state government department wants to study various characteristics of retail stores in the state. A random sample of 25 retail stores reveals that 8 of the stores sell women's fashion.

Construct a 95% confidence interval estimate of the population proportion of retail stores which sell women's fashion.

Question 17 (6 marks]

An experiment was conducted to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a group of people who drank alcohol and another group given a placebo.

The results are shown in the following table.

	n	Sample mean	Sample standard deviation
Alcohol (Treatment)	22	4.18	1.87
Placebo (Control)	22	2.09	1.74

Use a 5% significance level to test the claim that there is a difference in the average number of errors of the Alcohol group and Placebo group. Assume that both populations are normal with equal variances. You may use the following Excel printout.

Question 18 (7 marks)

A director of real estate sales, after several years of experience, decided that the best measure of effectiveness of a salesperson is the number of sales made, rather than, say, the value of their sales.

Four of her salespeople over the past year had the following results:

Person	A	B	C	D
Sales	12	16	10	14

At a 5% level of significance, can we conclude that the numbers of sales for each salesperson differ?

Question 19 (2 + 2 = 4 marks)

The owner of a local grocery store varied the price of a half-kilo loaf of bread for six consecutive weeks. The data below shows the price per loaf for each of these weeks, and the number of loaves sold that week.

Price (x)	$0.60	$0.62	$0.58	$0.60	$0.64	$0.62
Loaves sold (y)	220	200	280	250	190	240

You may use the following Excel print-outs or summary statistics provided to answer the questions.

SUMMARY OUTPUT			SUMMARY STATISTICS
Regression Statistics		n =	6
Multiple R	0.855		=	0.61
R Square	0.731		y =	230
Adjusted R Square	0.663		sx =	0.00044
Standard Error	19.424		sy =	1120
Observations	6		sxy =	-0.6
	Coefficients	Standard Error	t Stat	P-value
Intercept	1061.818	252.732	4.201	0.014
Price	-1363.636	414.111	-3.293	0.030

(a) Determine the estimated regression equation that can be used to predict the number of loaves sold given the price.

(b) Predict the number of loaves sold at a price of $0.65.

Question 20 (2 + 2 = 4 marks)

(a) The owner of a small caf that specialises in sandwiches has noticed that the prices of the ingredients for her BLT (Bacon, Lettuce and Tomato) sandwich have increased. She records the price of each ingredient in 2019 and in 2020.

	2019 Prices	2020 Prices
Bacon Strips (1 kg)	$13.00	$15.00
Lettuce (1 kg)	$3.00	$4.00
Tomato (1 kg)	$4.00	$7.00

Calculate a simple aggregate price index for 2020, taking 2019 as the base year.

(b) The owner of a small caf that specializes in cups of tea has noticed that the prices of the ingredients for her tea have increased. In 2020, she charged $4.50 for a cup of tea.

The owner went to the Australian Bureau of Statistics and noted the CPI for 2020 and 2021 as follows:

2020 108.20

2021 132.24

What should be the price of a cup of tea in 2021 to keep up with the effects of inflation?