Sin 20.sin 10 as sum or difference
1 answer:
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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!
see the attachment..........
<u>Answer- </u>Wendy spent 3 hours on the train
<u>Solution-</u>
The distance between the cities= 500 mi.
She traveled part of the way by bus, and other part by train.
The bus averaged 40 mph, and the train averaged 120 mph.
The entire trip took 6.5 hours.
let d = distance traveled by train
the total distance was given as 500 mi ,
therefore, distance traveled by bus = (500-d) mi
time = distance/speed
⇒ train traveling time + bus traveling time = 6.5 hrs
⇒
⇒ d + 3(500-d) = 120(6.5)
⇒ d + 1500 - 3d = 780
⇒ 2d = 720
⇒ d = 360 mi
so d = 360 mi by train
⇒ 360/120 = 3 hrs on the train