A biologist is interested in the relationship between susceptibility to certain carcinogens and gender. To test this hypothesis, a simple random sample of 1200 male rats is selected while, independently, a simple random sample of 1200 female rats is selected. The three carcinogens are the microbial carcinogen aflatoxin B₁ and two viral carcinogens, hepatitis B and human papillomavirus (HPV) , which have both been found to cause cancer in humans. The rats were randomly assigned to receive one of the three carcinogens, with each carcinogen being given to 400 rats of each gender. The following table summarizes the number of rats of each gender that developed a tumor under a given treatment:
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$\begin{array} { | l | c | c | } \hline & { \text { Gender } } \\\hline { \text { Carcinogen } } & \text { Male } & \text { Female } \\\hline \text { Aflatoxin } B _ { 1 } & 96 & 295 \\\hline \text { Hepatitis B } & 32 & 45 \\\hline \text { HPV } & 94 & 40 \\\hline\end{array}$ Using appropriate technology, what is the value of the chi-square statistic for this table?

Question

A biologist is interested in the relationship between susceptibility to certain carcinogens and gender. To test this hypothesis, a simple random sample of 1200 male rats is selected while, independently, a simple random sample of 1200 female rats is selected. The three carcinogens are the microbial carcinogen aflatoxin B₁ and two viral carcinogens, hepatitis B and human papillomavirus (HPV) , which have both been found to cause cancer in humans. The rats were randomly assigned to receive one of the three carcinogens, with each carcinogen being given to 400 rats of each gender. The following table summarizes the number of rats of each gender that developed a tumor under a given treatment:
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\begin{array} { | l | c | c | } \hline & { \text { Gender } } \\\hline { \text { Carcinogen } } & \text { Male } & \text { Female } \\\hline \text { Aflatoxin } B _ { 1 } & 96 & 295 \\\hline \text { Hepatitis B } & 32 & 45 \\\hline \text { HPV } & 94 & 40 \\\hline\end{array}

Using appropriate technology, what is the value of the chi-square statistic for this table?

Quizplus · Accepted Answer

The chi-square statistic for this table is calculated based on the observed frequencies of tumors in rats given different carcinogens by gender and the expected frequencies under the null hypothesis that gender does not affect susceptibility to these carcinogens. The calculation involves comparing the observed frequencies to the expected frequencies for each cell in the table and summing the squared differences divided by the expected frequencies. The value of 89.966 indicates a significant difference between genders in susceptibility to the carcinogens, suggesting that the null hypothesis can be rejected. This value is calculated using the formula for the chi-square test statistic, which involves summing the squared differences between observed and expected frequencies, divided by the expected frequencies for each cell in the table.

A Biologist Is Interested in the Relationship Between Susceptibility to Certain