The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below Age (years)Percent of Canadian PopulationObserved Number in the Village Under 57 2 485 to 1413 6 7015 to 6467 1 29065 and older12 1 47 Use a 5 level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village (a) What is the level of significance State the null and alternate hypotheses H 0 The distributions are the same H 1 The distributions are different H 0 The distributions are different H 1 The distributions are different H 0 The distributions are different H 1 The distributions are the same H 0 The distributions are the same H 1 The distributions are the same (b) Find the value of the chi square statistic for the sample (Round your answer to three decimal places ) Are all the expected frequencies greater than 5 Yes No What sampling distribution will you use Student's t normal uniform binomial chi square What are the degrees of freedom (c) 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 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories Since the P value , we fail to reject the null hypothesis Since the P value , we reject the null hypothesis Since the P value, we reject the null hypothesis Since the P value, we fail to reject the null hypothesis (e) Interpret your conclusion in the context of the application At the 5 level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population At the 5 level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 26, 2024

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.Age (years)Percent of Canadian PopulationObserved Number

in the VillageUnder 57.2%485 to 1413.6%7015 to 6467.1%29065 and older12.1%47

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: The distributions are the same.

H₁: The distributions are different.

H₀: The distributions are different.

H₁: The distributions are different.

H₀: The distributions are different.

H₁: The distributions are the same.

H₀: The distributions are the same.

H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

What sampling distribution will you use?

Student'st

normal

uniform

binomial

chi-square

What are the degrees of freedom?

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

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since theP-value >, we fail to reject the null hypothesis.

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

Since theP-value, we reject the null hypothesis.

Since theP-value, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.

At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.