QUESTION TWO [25 MARKS]

Your task is to interview a representative sample of attendees for the large concert venue where you work. The new season schedule includes 200 live concerts featuring all types of musicians and musical groups. Since neither the number of attendees nor their descriptive characteristics are known in advance, you decide on nonprobability sampling. Based on past seating congurations, you can calculate the number of tickets that will be available for each of the 200 concerts. Thus, collectively, you will know the number of possible attendees for each type of music. From attendance research conducted at concerts held by the Glacier Symphony during the previous two years, you can obtain gender data on attendees by type of music. How would you conduct a reasonably reliable nonprobability sampling?[5 marks]

A recent article in Nairobi Post Weekly Edition indicated that about 80% of the estimated Sh.200 billion of federal housing subsidies consists of tax breaks (mainly deductions for mortgage interest payments and preferential treatment for profits on home sales). Nairobi County housing benefits average Sh.8,268 for those with incomes between Sh.50,000 and Sh.200,000 and Sh.365 for those with income of Sh.40,000 to Sh.50,000. Suppose the standard deviations of the housing benefits in these two categories were equal to Sh.2,750 and Sh.120, respectively.

Examine the two standard deviations. What do these indicate about the range of benefits enjoyed by the two groups?[3 marks]

Repeat part (i) using the coefficient of variation as the measure of relative variation.[3 marks]

The closing prices of Kenol stock, adjusted for splits and dividends, for the final trading days of December 2012-2016 are given in the following table. The consumer price index (CPI) for December of each year is also given. Deflate the stock price series and comment on the financial performance of Kenol stock.[4 marks]

Year

Price (Sh.)

CPI

2012

19.50

179.3

2013

21.70

182.1

2014

23.50

215.3

2015

39.80

233.8

2016

52.30

242.3

Men have a reputation for not wanting to ask for directions. A study that was conducted indicated that 42% of men and 61% of women would stop and ask for directions. The Kenya NationalBureau of Statistics 2019 population estimate was that for individuals 18 or over, 48.2% were men and 51.8% were women.

A randomly chosen driver gets lost on a road trip. Determine the probability that the driver is a woman and stops to ask for directions. [2 marks]

Calculate the probability that the driver stops to ask for directions. [2 marks]

Given that a driver stops to ask for directions, determine the probability that the driver was a man.[2 marks]

The table below shows the prices and quantities of foodstuffs consumed by homesteads over the past four years in certain region. Determine the Fisher's ideal price index for 2019 using year 2018 as the base year.[4 marks]

Foodstuffs

Year

2018

2019

Price/kg (Sh.)

Quantity (kg)

Price/kg (Sh.)

Quantity (kg)

Alpha

75

45

90

90

Beta

135

105

165

80

Chi

105

120

135

95