Question

Please give me step by step answer how to solve this question:

Consider the following example. In a study reported in the California Journal of Nursing, nurses were asked to report their degree of job-related stress. They were asked 20 questions about their work and they responded on a 1-5 scale as the amount of stress they felt (5 being the most). These responses were added up in order to come up with a numeric measure of job stress. Below is the Table with 2 of the groups' data: LVN and RN. Consider the following example. In a study reported in the California Journal of Nursing, nurses were asked to report their degree of job-related stress. They were asked 20 questions about their work and they responded on a 1-5 scale as the amount of stress they felt (5 being the most). These responses were added up in order to come up with a numeric measure of job stress. Below is the Table with 2 of the groups' data: LVN and RN. What do you make of this?

LVN	RN
78	43
41	63
68	60
69	52
54	54
62	73
76	68
56	57
61	61
65	70
64	50
69	37
79	73
75	74
75	58

Answer 1

n₁ = 15

₁ = 66.13

s₁ = 10.39

n₂ = 15

₂ = 59.53

s₂ = 11.13

Let's conduct a hypothesis for equality of variances of the two population:

H₀: ₁² = ₂²

H₁: ₁²    ₂²

Formula Used:

F = 0.871

p-value for F_14,14= 0.6 > 0.05 i.e H₀ can't be rejected and hence we can say that variances of the two populaitons' are equal.

Now,

Let's test the hypothesis that mean stress level in group LVN is different from stress in group RN.

H₀: ₁ = ₂  

H₁: _1  2

Formula Used:

Assumptions: Populations are normally distributed and the populations' variances are equal (proved above)

t = 1.679

df = 15 + 15 - 2

= 28

p-value = 0.1043 > 0.05 i.e H₀ can't be rejected and hence we can say that mean stress level among nurses from the two groups is not different.

Thus we can say that the aggregate stress scores are sampled from a single population (as mean and variance of both the groups are same)

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