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, 13% were in the 20- to 35-year-old bracket, 32% 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 29 28 67 65 21 (i) Give the value of the level of significance. State the null and alternate hypotheses. 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: 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 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: 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. (Round your answer to three decimal places.) (iv) Conclude the test. Since P-value , we reject the null hypothesis. hypothesis. Since P-value < , we do not reject the null Since P-value , we do not reject the null hypothesis. Since P-value < , 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