Question

STATISTICS HYPOTHESIS

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) and a similar sample consisting of the clients without X ancestry. Then, Jennifer was asked to compare clients' Y parameters 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 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 2.1(and the population variance is equal to 4.41). 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? Or the chances are equal (on average Y parameters are the same)? Help Jennifer Nguyen to conduct the test. Use Data Analysis z-Test: Two-Sample for Means. Note Data below

a) Describe the claim

b) Test Statistics

Critical Value

P-value

c) Decision

Data below

	Y-scores
	X Group	Not X Group
1	9.2	2.6
2	6.4	4.7
3	5.5	8.8
4	7.1	2.0
5	3.6	1.2
6	5.3	3.5
7	6.5	5.2
8	9.8	6.8
9	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
39	5.5	2.1
40	5.8	8.7

Answer 1

ม different Hi: M1-M ₂ to a) claim - The risk of developing canveer is diffe for a ponon belonging to the group (ethnic) to not X group compared pesson belonging (no ethnic ancestory). :M,-42 to a b Hoi =0 x group a For the x xi mean) = 6.1575 For the not x group, Tz (mean) = 4.4825 Test statistic (zo) = x, X2 6-1575 - 4.4825 = o2 o m n + 4.41 40 + 9 40 s Test statistic (Z.) 2.893 Critical value (Sounce Zal = 70.000 Ca-sicked) [camere attached Sounce - 2.576 STATKEY Cimape attacked) Source - STATKEY attacked) p-value = 0.0038 Decision - ツ Using the p-value approach, pralue (0.0038) <Q (0.01), We Rejest the Null hypothesis at 1% level of significance and conclude that the claim that the risk developing W cancer is different for a person of lethue ancestory) compared group/ no ethnic ancestory) X group to person of truu. دن not x

StatKey Theoretical Distribution Normal Distribution- Reset Plot Normal Distribution Left Tail Two-Tail Right Tail 0.40 Mean Standard Deviation 0 0.35 Edit Parameters 0.30 0.25 0.20 0.0050 0.990 0.0050 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 -2.576 2.576 Activate Windows

Statkey Theoretical Distribution Normal Distribution- Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 0.35 Edit Parameters 0.30 0.25 0.20 0.0019 0.996 0.0019 0.15 0.10 0.05 0.00 -4.0 -2.0 -1.0 0.0 1.0 2.0 4.0 13.0 2.893 -2.893 Activate Windows

The test statistic is calculated using the formula mentioned. The critical value and the p value is obtained from STATKEY (images attached for reference). We compare the p value with alpha and make the required decision.