MATH235 MATH235 Week 1 - Assessed problems (coursework) MATH235 Week 2 - Workshop problems

MATH235 Week 1 - Moodle Quiz-assessed problems

The following quiz questions use the data in Table 0.3. The aim is to test the hypothesis that the mean price of sugar is not equal to 14 cents per lb. Assume that the data are an IID sample from a Normal $(\mu,\sigma^{2})$ distribution, with $\sigma^{2}=28.8$ known.

Year	Coffee	Sugar	Tea
1995	151.2	13.3	1.4
1996	122.1	12.0	1.7
1997	189.1	11.4	2.0
1998	135.2	8.9	2.0
1999	103.9	6.3	1.8
2000	87.1	8.2	1.9
2001	62.3	8.6	1.6
2002	61.5	6.9	1.5
2003	64.2	7.1	1.5
2004	80.5	7.2	1.7
2005	114.9	9.9	1.6
2006	114.4	14.8	1.9
2007	123.5	10.1	2.1
2008	139.8	13.1	2.3
2009	143.9	16.9	2.7
2010	196.0	21.1	2.9
2011	275.3	25.9	2.9
2012	230.0	21.1	2.6
2013	182.3	16.6	2.5
2014	180.0	16.0	2.4
2015	175.0	15.5	2.2

Table 0.3: Forecasts of annual prices for coffee (cents per lb), sugar (cents per lb) and tea (dollars per kg) from 1995 to 2015. Data provided by the Economist Intelligence Unit.

Q1.1

Sample mean
What is the sample mean for sugar prices?

(a)

2.58
(b)

12.5
(c)

12.9
(d)

13.2
(e)

13.6

[marks: 2]

Q1.2

Test statistic
What is the value of the test statistic to test $H_{0}:\mu=14$ against $H_{1}:\mu\neq 14$ ?

(a)

-0.917
(b)

-0.171
(c)

-0.939
(d)

-0.175
(e)

0.939

[marks: 2]

Q1.3

Critical value
Assuming a 5% significance level, what is the critical value for this test?

(a)

1.28
(b)

1.96
(c)

2.00
(d)

1.64
(e)

2.09

[marks: 2]

Q1.4

p value
What is the $p$ -value for your test?

(a)

0.348
(b)

0.360
(c)

0.174
(d)

0.179
(e)

0.823

[marks: 2]

Q1.5

Conclusion
What is the correct conclusion to be drawn from your analysis?

(a)

There is evidence in favour of a mean price less than 14 cents per lb.
(b)

There is evidence in favour of a mean price greater than 14 cents per lb.
(c)

There is evidence that the mean price is not 14 cents per lb.
(d)

There is no evidence against a mean price of 14 cents per lb.

[marks: 2]