A sociologist is studying the age of the population in Blue Valley. Ten years ag
ID: 3160448 • Letter: A
Question
A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 20% were under 20 years old, 14% were in the 20- to 35-year-old bracket, 31% were between 36 and 50, 24% were between 51 and 65, and 11% 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?
23
1. Find the sample test statistic. (Round your answer to two decimal places.)
2.Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)
Under 20 20 - 35 36 - 50 51 - 65 Over 65 28 26 68 6523
Explanation / Answer
1.
Doing an observed/expected value table,
O E (O - E)^2/E
28 42 4.666666667
26 29.4 0.393197279
68 65.1 0.129185868
65 50.4 4.229365079
23 23.1 0.0004329
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 9.418847793 [ANSWER]
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2.
As df = a - 1,
a = 5
df = a - 1 = 4
Hence, the p value is, by technology,
p = 0.05144172 [ANSWER, P VALUE]
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