It 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) (Group 1) and a similar sample consisting of the clients without X ancestry (Group 2). Then, Jennifer was asked to compare clients' Y scores indicating likelihood of developing W cancer. (As the matter is ticklish, we will not be naming the ethnic group, the type of cancer, the medical scores, and the gender of sample members). It is known that the standard deviation of population Y scores for X group (group 1) is 2.0 (therefore the population variance is equal to 4.0). The standard deviation of population Y scores for "not X" group (group 2) is 3.0 (therefore the population variance is equal to 9.0). This assumption allows using z-distribution. The data are provided in the data file. 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 (that is, whether the mean Y scores are the same for these two groups)? Help Jennifer Nguyen to conduct the hypothesis test. Use Data Analysis z-Test: Two-Sample for Means.

Data for Problem 4 Y-scores X Group (Group 1) Not X Group (Group 2) 9.2 2.6 W NE 6.4 4.7 5.5 8.8 7.1 2.0 3.6 1.2 5.3 3.5 6.5 5.2 9.8 6.8 2.5 9.1 10 4.9 1.0 11 9.5 0.8 12 7.7 0.9 13 8.1 1.6 14 6.0 4.5 15 5.0 5.6 16 5.5 7.5 17 7.2 2.8 18 4.5 2.0 19 4.0 1.9 20 4.8 1.8 21 8.5 8.5 22 6.6 7.4 23 7.1 8.0 24 3.6 9.5 25 4.7 2.4 26 6.2 0.9 27 9.1 1.4 28 5.5 8.3 29 5.9 5.0 30 6.0 7.7 31 7.1 9.2 32 4.0 1.6 33 5.0 4.5 34 5.5 5.5 35 7.2 7.5 36 4.5 2.9 37 6.2 2.0 38 9.2 1.9