Cancer

The data below summarize the stage of disease at diagnosis for women with breast cancer by age and race.

stage of breast cancer at diagnosis by age and race

You can use the Distribution Calculators page in SALT to find critical values and$/$or $p-$values to answer parts of this question. Please note that the

Inferential Statistics page does not use the continuity$-$corrected version of the test statistic.

$($a$)$ Test whether the distribution of stage of disease is significantly different between Caucasian and African American women with breast cancer

who are younger than $50$ years of age. Please provide a p$-$value $($two$-$tailed$).$ Ignore the unstaged cases in your analysis. $($Let female African

Americans who are younger than $50$ years of age be population $1$ and female Caucasians who are younger than $50$ years of age be population $2.)$

Select the appropriate null and alternative hypotheses.

$H_0$ : The proportions falling into each of the three stage categories are the same for both female Caucasians and female African

Americans.

$H_1$ : The proportions for at least one of the stage categories is different for female Caucasians and female African Americans.

$H_0$ : The proportions for at least one of the stage categories is different for female Caucasians and female African Americans.

$H_1$ : The proportions falling into each of the three stage categories are the same for both female Caucasians and female African

Americans.

Calculate the test statistic. $($Round your answer to two decimal places.$)$

Use technology to calculate the $p-$value. $($Round your answer to four decimal places.$)$

$p-$value $=$

x

State the conclusion in the problem context. $($Use $=0\mathrm{.}05.)$

Reject $H_0.$ There is not sufficient evidence to conclude that the distribution of stage of disease is significantly different between

Caucasian and African American women with breast cancer who are younger than $50$ years of age.

Fail to reject $H_0.$ There is not sufficient evidence to conclude that the distribution of stage of disease is significantly different between

Caucasian and African American women with breast cancer who are younger than $50$ years of age.

Reject $H_0.$ There is sufficient evidence to conclude that the distribution of stage of disease is significantly different between Caucasian

and African American women with breast cancer who are younger than $50$ years of age.

Fail to reject $H_0.$ There is sufficient evidence to conclude that the distribution of stage of disease is significantly different between

Caucasian and African American women with breast cancer who are younger than $50$ years of age.

$($b$)$ The $5-$year survival rates by stage of disease, age at diagnosis, and race are provided in the table below.

five$-$year survival rates for breast cancer by stage at diagnosis, age at

diagnosis, and race

Test whether the $5-$year survival rate for breast cancer is significantly different between female African Americans and female Caucasians who

are younger than $50$ years of age and have localized disease. Provide a p$-$value $($two$-$tailed$).($Let female African Americans who are younger than

$50$ years of age be population $1$ and female Caucasians who are younger than $50$ years of age be population $2.)$

State the hypotheses to be tested. $($Enter $$ for $$ as needed.$)$

$H_0$:

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$H_1$

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Find the test statistic. $($If the test does not have a defined test statistic, enter DNE. Round your answer to two decimal places.$)$