Question

A social psychologist suspects that people who serve on juries tend to be much older than citizens in the general population are. Jurors are selected from the list of registered voters, so the ages for jurors should have the same distribution as the ages for voters. The psychologist obtained voter registration records and found that 20% of registered voters are between 18 and 29 years old, 35% are between 30 and 49 years old, and 45% are age 50 or older. The psychologist also monitored jury composition over several weeks and observed the following distribution of ages for actual juries:

Age Categories for Jurors
18 – 29	30 – 49	50 and Over
12	23	45

Are the data sufficient to conclude that the age distribution for jurors is significantly different from the distribution for the population of registered voters?

1. What are the hypotheses?

2. Specify the degrees of freedom and critical value(s) using α = 0.05.  

3. Conduct the proper test.

4. What do you conclude?

Answer 1

Ans:

H0:The age distribution for jurors is same as the distribution for the population of registered voters.

Ha: The age distribution for jurors is different from the distribution for the population of registered voters.

Category	fo	pi	fe	(fo-fe)^2/fe
18-29	12	0.2	16	1.000
30-49	23	0.35	28	0.893
50 or over	45	0.45	36	2.250
Total	80	1	80	4.143

Test statistic:

Chi square=4.143

df=3-1=2

criitcal value=CHIINV(0.05,2)=5.991

P-value=CHIDIST(4.143,2)=0.1260

Fail to reject the null hypothesis,as test statistic is less than critical value.

There is not sufficient evidence to conclude that the age distribution for jurors is significantly different from the distribution for the population of registered voters