Suppose a researcher has collected sample data on beer price (in $/per litre) and per capita beer quantity consumed (in litres) in Australia between 1975-2017. Using EXCEL, answer the following questions.

Beer price and quantity

Year - Beer Price (in $/per litre) - Beer Quantity (in litres)

1975 - 1.85 - 191.32

1976 - 2.32 - 192.14

1977 - 2.54 - 187.13

1978 - 2.67 - 186.62

1979 - 3.09 - 182.79

1980 - 3.35 - 176.45

1981 - 3.65 - 177.44

1982 - 4.02 - 172.69

1983 - 4.58 - 171.03

1984 - 5.02 - 161.08

1985 - 5.44 - 155.14

1986 - 5.91 - 149.97

1987 - 6.52 - 150.31

1988 - 7.12 - 143.92

1989 - 7.25 - 145.88

1990 - 7.70 - 148.45

1991 - 8.32 - 146.19

1992 - 8.61 - 141.71

1993 - 8.87 - 133.26

1994 - 9.16 - 127.46

1995 - 9.44 - 125.42

1996 - 9.95 - 123.97

1997 - 10.22 - 121.84

1998 - 10.29 - 122

1999 - 10.46 - 120.59

2000 - 10.68 - 118.99

2001 - 11.63 - 117.6

2002 - 11.94 - 117.77

2003 - 12.32 - 114.28

2004 - 13.10 - 115.58

2005 - 13.69 - 111.03

2006 - 14.33 - 108.78

2007 - 14.91 - 108.79

2008 - 15.71 - 108.69

2009 - 16.41 - 108.35

2010 - 17.32 - 107.98

2011 - 17.83 - 104.94

2012 - 18.25 - 100.57

2013 - 18.62 - 96.51

2014 - 19.16 - 93.02

2015 - 19.71 - 92.38

2016 - 20.44 - 86.49

2017 - 20.99 - 89.43

Source: Australian Bureau of Statistics

Questions:

(a) Prepare a numerical summary output for the two variables; beer price and per capita beer quantity consumed and explain the key numerical descriptive measures

(b) Based on the numerical descriptive measures, comment on the shape of the distribution of the two variables; beer price and per capita beer quantity consumed.

(c) Test the hypothesis that the population mean per capita beer consumption is less than 135 litres/year.

(d) If the researcher claims that the population mean per capita beer consumption is greater than 135 litres/year do you agree with that? Explain why.

(e) Based on part (c) and (d), what can you say about the population mean per capita beer consumption in Australia?