Question

A political scientist believes that, in recent years, the ethnic composition of the city he studies lives has changed over recent years. The most current figures (collected a few years ago) show that the inhabitants were 53% Norwegian, 32% Swedish, 8% Irish, 5% German and 2% Italian. To test his belief, a random sample of 750 inhabitants is taken and the results are shown in the table below. Note that the “total” column is not observed data but a number provided to help you compute the expected values for this data. (Use a χ2 statistic and α = 0.05)

Norwegian	Swedish	Irish	German	Italian	Total
399	193	63	82	13	750

1. What is the null hypothesis?
2. What do you conclude about the population?
3. Have the population demographics actually shifted?
4. Report your obtained χ² in proper statistical reporting format.

Answer 1

Ans:

Chi square test for goodness of fit:

a)

H₀:The given sample data fits the recent demographic distribution.

b)

	Percentage	Observed(fo)	Expected(fe)	(fo-fe)^2/fe
Norwegian	53.00%	399	397.5	0.006
Swedish	32.00%	193	240	9.204
Irish	8%	63	60	0.150
German	5.00%	82	37.5	52.807
Italian	2.00%	13	15	0.267
Total	100.00%	750	750.00	62.433

Test statistic:

Chi square=62.433

df=5-1=4

p-value=CHIDIST(62.433,4)=0.0000

Reject the null hypothesis.

c)There is sufficient evidence to conclude that the give data does not fit the recent demographic distribution.

We can say that  the population demographics have actually shifted.

d)Chi square(4)=62.433,p<0.0001,significant