A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that19%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, and12%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 67 66 22

(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: Time ten years ago and today are independent.

H₁: Time ten years ago and 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 population 10 years ago and the population today are independent.

H₁: The population 10 years ago and the population today are not independent.

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

(iii) Find or estimate theP-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 theP-value, we do not reject the null hypothesis.

Since theP-value <, we do not reject the null hypothesis.

Since theP-value <, we reject the null hypothesis.

Since theP-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.

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Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of21roller bearings from the old manufacturing process showed the sample variance of diameters to bes²=0.233.

Another random sample of27roller bearings from the new manufacturing process showed the sample variance of their diameters to bes²=0.144.

Use a 5% level of significance to test the claim that there is a difference (either way) in the population variances between the old and new manufacturing processes.

Classify the problem as being a Chi-square test of independence or homogeneity, Chi-square goodness-of-fit, Chi-square for testing or estimating²or,Ftest for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.

One-way ANOVA

Two-way ANOVA

Chi-square test of independence

Ftest for two variances

Chi-square test of homogeneity

Chi-square goodness-of-fit

Chi-square for testing or estimating²or

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

State the null and alternate hypotheses.

H₀:₁²=₂²;H₁:₁²>₂²

H₀:₁²=₂²;H₁:₁²₂²

H₀:₁²<₂²;H₁:₁²=₂²

H₀:₁²=₂²;H₁:₁²<₂²

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

(iii) Find theP-value of the sample test statistic.

P-value > 0.200

0.100 <P-value < 0.200

0.050 <P-value < 0.100

0.020 <P-value < 0.050

0.002 <P-value < 0.020

P-value < 0.002

(iv) Conclude the test.

Since theP-value is greater than or equal to the level of significance= 0.05, we fail to reject the null hypothesis.

Since theP-value is less than the level of significance= 0.05, we reject the null hypothesis.

Since theP-value is less than the level of significance= 0.05, we fail to reject the null hypothesis.

Since theP-value is greater than or equal to the level of significance= 0.05, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to show that the variance for the new manufacturing process is different.

At the 5% level of significance, there is sufficient evidence to show that the variance for the new manufacturing process is not different.

At the 5% level of significance, there is insufficient evidence to show that the variance for the new manufacturing process is not different.

At the 5% level of significance, there is sufficient evidence to show that the variance for the new manufacturing process is different.