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, 11% were in the 20- to 35-year-old bracket, 32% were betwee
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, 11% were in the 20- to 35-year-old bracket, 32% were between 36 and 50, 24% were between 51 and 65, and 13% 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 27 27 65 66 25(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. (Round your answer to three decimal places.)(iv) Conclude the test.Since P-value ≥ α, we reject the null hypothesis.Since P-value < α, we reject the null hypothesis. Since P-value < α, we do not reject the null hypothesis.Since P-value ≥ α, we do not 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.
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