A sociologist is studying the age of the population in Blue Valley. Ten years ag

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, 12% were in the 20. to 35-year-old bracket, 31% were between 36 and 50, 24% were between Si and 65, and i 2% were over 6S. 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 28 25 23 (1) Give the value of the level of significance. State the null and alternate hypotheses O Ho: The distributions for the population 10 years ago and the population today are the same. Hs: The distributions for the population 10 years ago and the population today are different. HO: Time ten years ago and today are independent. H: Time ten years ago and today are not independent O Ho: Ages under 20 years old, 20- to 35-year-old, between 36 and S0, between 51 and 65, and over 65 are independent. Hs: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are not independent. O Ho: The population 10 years ago and the population today are independent. H1: The population 10 years ago and the population today are not independent. (i)Find the sample test statistic. (Round your answer to two decimal places.) l) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) (iv) Conclude the test. O Since P-value

Explanation / Answer

i) The value of level of significance is 0.01

ii) Null Hypothesis: The distribution for the population 10 years ago and the population today are same.

Against

Alternative Hypothesis: The distribution for the population 10 years ago and the population today are not same.

### By using R command

> X=c(28,25,68,66,23)
> X
[1] 28 25 68 66 23
> chisq.test(X)

Chi-squared test for given probabilities

data: X
X-squared = 49.952, df = 4, p-value = 3.694e-10

X-squared = 49.952

p-value = 3.694e-10

iv)  p-value < alpha we reject the null hypothesis.

v) at 1% level of significance, there is sufficient evidence to claim that the age distribution of the population of Blue Valley has changed.

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