t appears that not all people are equally vulnerable to cancer. People from some ethnic groups have higher or lower than average chances of developing certain types of cancer. Jennifer’s manager Dr. Steinberg thinks that the company’s insurance policy should reflect this fact and constantly raises this question in the meetings. To be more convincing, he asked Jennifer Nguyen to take a random sample of those Healthy Life clients who belong to ethnic group X (at least on their maternal or paternal side) and a similar sample consisting of the clients without X ancestry. Then, Jennifer was asked to compare clients' indicators which indicate the likelihood of developing W cancer. (As the matter is ticklish, we will not be naming the ethnic group, the type of cancer, the medical parameter, and the gender of sample members.) Then, it is known that in the general population Y parameters are distributed with the standard deviation of 3.0 (therefore the population variance is equal to 9.0). However, in the X ethnic group the population standard deviation is about 2 (and the population variance is equal to 4). As only 2-3% of Canadians have X ancestors, Jennifer and her manager assume that the standard deviation in the population of those who have no X ancestry is also around 3.0 as in the country in general. This assumption allows using z-distribution. The data are provided. Can we state at 1% level of significance that it matters whether a person belongs to X group or not in terms of the risk of developing W cancer? Help Jennifer Nguyen to conduct the test. Use Data Analysis z-Test: Two- Sample for Means.
t appears that not all people are equally vulnerable to cancer. People from some ethnic groups have higher or lower than average chances of developing certain types of cancer. Jennifer’s manager Dr. Steinberg thinks that the company’s insurance policy should reflect this fact and constantly raises this question in the meetings. To be more convincing, he asked Jennifer Nguyen to take a random sample of those Healthy Life clients who belong to ethnic group X (at least on their maternal or paternal side) and a similar sample consisting of the clients without X ancestry. Then, Jennifer was asked to compare clients' indicators which indicate the likelihood of developing W cancer. (As the matter is ticklish, we will not be naming the ethnic group, the type of cancer, the medical parameter, and the gender of sample members.) Then, it is known that in the general population Y parameters are distributed with the standard deviation of 3.0 (therefore the population variance is equal to 9.0). However, in the X ethnic group the population standard deviation is about 2 (and the population variance is equal to 4). As only 2-3% of Canadians have X ancestors, Jennifer and her manager assume that the standard deviation in the population of those who have no X ancestry is also around 3.0 as in the country in general. This assumption allows using z-distribution. The data are provided. Can we state at 1% level of significance that it matters whether a person belongs to X group or not in terms of the risk of developing W cancer? Help Jennifer Nguyen to conduct the test. Use Data Analysis z-Test: Two- Sample for Means.
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