There are four political parties in Eurelia: Recidivist, Atavist, Ergodist, and Anachronist. A pollster desires to learn if the political party supported depends significantly on whether the voter is urban or rural. The following preliminary data have been collected. What conclusion will the pollster draw?

	Recidivist	Atavist	Ergodist	Anachronist
Rural	10	22	20	26
Urban	20	28	40	34

b) In the last election the Recidivists got 22% of the vote, the Atavists got 30%, the Ergodists got 35%, and the Anachronists got 13%. Test whether the proportions are now significantly different from those in the last election, based on the poll results above.

ECON 227

4. In Eurelia three of the four political parties agreed to the following study. Small independent random samples of Eurelian voters were selected, and the table below was compiled.

Some initial computations have been made.

For the Atavist voters in the table the sum of their incomes is 186, and the sum of the squares of their incomes is 7474.

For the Recidivist voters in the table the sum of their incomes is 277, and the sum of the squares of their incomes is 11327.

For the Anachronist voters in the table the sum of their incomes is 371, and the sum of the squares of their incomes is 16601.

Party Affiliation	Income ($1000s)	Age	Party Affiliation	Income ($1000s)	Age
Atavist	23	26	Recidivist	40	39
Atavist	34	33	Anachronist	47	50
Atavist	32	35	Anachronist	45	44
Atavist	54	53	Anachronist	38	41
Atavist	43	46	Anachronist	46	45
Recidivist	35	34	Anachronist	43	46
Recidivist	33	36	Anachronist	28	27
Recidivist	55	54	Anachronist	34	37
Recidivist	44	47	Anachronist	23	22
Recidivist	36	35	Anachronist	67	70
Recidivist	34	37

ECON 227

a) Test whether there is a significant difference in the mean incomes amongst voters of the three political parties.

b) Give the theoretical requirements for the test you performed in a)

c) Construct a 90% CI (confidence interval) for the mean income of Recidivist-Party affiliates.

d) Test whether income and age are significantly correlated.

5. A government commission in Eurelia has collected some data on job satisfaction in independent random samples of workers on fixed hours (500 workers) versus flex time (300 workers).

	Fixed Hours	Flex Time
Satisfied	245	105
Not Satisfied	255	195

a) How large a sample is needed to form a 94% confidence interval for the proportion of satisfied workers amongst those on fixed hours? The desired margin of error is 2 percentage points.

b) Use the p-value method to test whether the proportion of satisfied workers amongst those on flex time significantly exceeds the proportion of satisfied workers amongst those on fixed hours.

c) Test whether the whether the proportion of satisfied workers amongst those on flex time significantly exceeds 50%.

ECON 227

6. Independent random samples of university students were selected from MacMillan University and LUniversit dEurlie. Here are some of the data that were collected on daily coffee consumption.

	MU	U dE
sample size	8	12
mean coffee consumption	560 ml	625 ml
standard deviation	68 ml	22 ml

a) Test whether the variances are significantly different.

b) Test whether the standard deviation in daily coffee consumption in MacMillan University significantly exceeds 34 ml.

c) Form a 95% CI (confidence interval) for the difference in mean coffee consumption.

d) Estimate the standard error of the difference of the sample means.