Describe the relationships among the four terms angle bisector, angle, ray, and line
1 answer:
First of all, the angle bisector, ray and angle line are all lines. Please refer to the picture attached. All of these lines are joined at one point called vertex which is at point O. The angle bisector is the line that divides the total angle into half. In this case, that would be line OB. The ray and line are the two legs of the angle, which are line OA and line OC, respectively. The angle is the arc between the lines.
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Answer:
a)
H₀: ρ₁ ≤ ρ₂
H₁: ρ₁ > ρ₂
b)
Z= ≈ N(0;1)
c)
p-value < .00001
d)
Reject the null hypothesis.
The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.
Step-by-step explanation:
Hello!
The objective is to test if the population proportion of vinyl gloves that leak viruses (population 1) is greater then the population proportion of latex gloves that leak viruses (population 2).
Sample 1 (Vinyl)
n₁= 225
Sample proportion 'ρ₁= 0.60
Sample 2 (Latex)
n₂= 225
Sample proportion 'ρ₂= 0.09
Pooled proportion: 'ρ= (x₁+x₂)/(n₁+n₂)= ( 'ρ₁ + 'ρ₂)/2= (0.60 + 0.09)/2= 0.345 ≅0.35
The hypothesis is:
H₀: ρ₁ ≤ ρ₂
H₁: ρ₁ > ρ₂
α: 0.05
The statistic to use is a pooled Z
Z= ≈ N(0;1)
The critical region is one-tailed to the right (positive), the critical value is:
If Z ≥ 1.64, you will reject the null hypothesis.
If Z < 1.64, you will not reject the null hypothesis.
Z= = 11.34
Since the calculated Z- value is greater than the critical value, the decision is to reject the null hypothesis. The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.
P-value approach:
p-value < .00001
If you compare with the level of signification, you reach the same decision.
I hope it helps!