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, 13%were in the 20- to 35-year-old bracket, 30% 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 | 26 | 67 | 65 | 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:
Time ten years ago and today are independent.
H1: Time ten years ago and today 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 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 do not reject the null hypothesis. Since P-value ≥ α, we 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.
Ans:
a)
level of significance=0.01
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)
Class | Observed(fo) | pi | Expected(fe) | (fo-fe)^2/fe |
Under 20 | 27 | 0.2 | 42 | 5.36 |
20-35 | 26 | 0.13 | 27.3 | 0.06 |
36-50 | 67 | 0.3 | 63 | 0.25 |
51-65 | 65 | 0.24 | 50.4 | 4.23 |
over 65 | 25 | 0.13 | 27.3 | 0.19 |
Total | 210 | 1 | 210 | 10.10 |
Test statistic:
Chi square=10.10
c)df=5-1=4
p-value=CHIDIST(10.10,4)=0.039
d)Since P-value ≥ α, we do not reject the null hypothesis.
e)At the 1% level of significance, there is insufficient evidence to claim that the age distribution of the population of Blue Valley has changed.
Get Answers For Free
Most questions answered within 1 hours.