Question

A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 19% 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 12% 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 25 25 66 65 29

(i) Give the value of the level of significance.

State the null and alternate hypotheses. 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. 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. 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. 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. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005

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

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

Answer 1