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

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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, 33% were between 36 and 50, 24% 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
29 26 68 67 20
(i) Give the value of the level of significance.

State the null and alternate hypotheses.
a.H0: The distributions for the population 10 years ago and the population today are the same.
H1: The distributions for the population 10 years ago and the population today are different.
b.H0: The population 10 years ago and the population today are independent.
H1: The population 10 years ago and the population today are not independent.
c.H0: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are independent.
H1: Ages under 20 years old, 20- to 35-year-old, between 36 and 50, between 51 and 65, and over 65 are not independent.
d.H0: Time ten years ago and today are independent.
H1: Time ten years ago and today are not independent.

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

(iii) Find or estimate the P-value of the sample test statistic.
a.P-value > 0.100
b.0.050 < P-value < 0.100
c.0.025 < P-value < 0.050
d.0.010 < P-value < 0.025
e.0.005 < P-value < 0.010
f.P-value < 0.005

(iv) Conclude the test.
a.Since the P-value < α, we reject the null hypothesis.
b.Since the P-value ≥ α, we do not reject the null hypothesis.
c.Since the P-value ≥ α, we reject the null hypothesis.
d.Since the P-value < α, we do not reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.
a.At the 1% level of significance, there is insufficient evidence to claim that the age distribution of the population of Blue Valley has changed.
b.At the 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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