Question

A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 21% were under 20 years old, 14% were in the 20- to 35-year-old bracket, 30% were between 36 and 50, 25% were between 51 and 65, and 10% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

Under 20	20 - 35	36 - 50	51 - 65	Over 65
27	27	69	68	19

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

Answer 1

Solution :

=> From the given information,

Age Frequency probability expected frequency (O - E)^2 (O - E)^2/E
group (O) (p) (E = n*p)

under 20 27 0.21 210*0.21 = 44.1 292.41 6.6306

20 - 35 27 0.14 210*0.14 = 29.4 5.76 0.1959

36 - 50 69 0.30 210*0.30 = 63 36 0.5714

51 - 65 68 0.25 210*0.25 = 52.5 240.25 4.5762

over 65 19 0.10 210*0.10 = 21 4 0.1905

=> Total n = 210

==> Test statistic (X^2) = Σ(O - E)^2/E

= 6.6306 + 0.1959 + 0.5714 + 4.5762 + 0.1905

= 12.1646

= 12.16 (rounded)