Answer:
Test statistic |Z| = 0.1040 < 1.96 at 0.05 level of significance
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that a report on the nightly news broadcast stated that 10 out of 108 households with pet dogs were burglarized
First proportion
![p_{1} = \frac{x_{1} }{n_{1} } = \frac{10}{108} = 0.0925](https://tex.z-dn.net/?f=p_%7B1%7D%20%3D%20%5Cfrac%7Bx_%7B1%7D%20%7D%7Bn_%7B1%7D%20%7D%20%3D%20%5Cfrac%7B10%7D%7B108%7D%20%3D%200.0925)
Given that a report on the nightly news broadcast stated that 20 out of 208 households without pet dogs were burglarized
Second proportion
![p_{2} = \frac{x_{2} }{n_{2} } = \frac{20}{208} = 0.0961](https://tex.z-dn.net/?f=p_%7B2%7D%20%3D%20%5Cfrac%7Bx_%7B2%7D%20%7D%7Bn_%7B2%7D%20%7D%20%3D%20%5Cfrac%7B20%7D%7B208%7D%20%3D%200.0961)
where
![P = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1} +n_{2} }](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7Bn_%7B1%7Dp_%7B1%7D%20%2Bn_%7B2%7Dp_%7B2%7D%20%20%20%7D%7Bn_%7B1%7D%20%2Bn_%7B2%7D%20%7D)
P = 0.09486
Q = 1 - P = 1 - 0.09486 = 0.90514
<u><em>Step(ii):-</em></u>
Test statistic
![Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bp_%7B1%7D-p_%7B2%7D%20%20%7D%7B%5Csqrt%7BPQ%28%5Cfrac%7B1%7D%7Bn_%7B1%7D%20%7D%20%2B%5Cfrac%7B1%7D%7Bn_%7B2%7D%20%7D%20%29%7D%20%7D)
![Z = \frac{0.0925-0.0961 }{\sqrt{0.09486 X 0.90514(\frac{1}{108 } +\frac{1}{208 } )} }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B0.0925-0.0961%20%20%7D%7B%5Csqrt%7B0.09486%20X%200.90514%28%5Cfrac%7B1%7D%7B108%20%7D%20%2B%5Cfrac%7B1%7D%7B208%20%7D%20%29%7D%20%7D)
Z = -0.1040
|Z| = |-0.1040|
|Z| = 0.1040
Critical value Z = 1.96 at 0.05 level of significance
@@@<---?@<------12
12*3=36
He used 36 nails
Answer: b = 14 or the absolute value form is -14
Step-by-step explanation:
take it out of absolute value form
b-5=9
add 5 to both sides
b = 14 or the absolute value form is -14
Answer:
240 cubes
Step-by-step explanation:multiply all sides then divide by1/2
4x10x3=120
120/1/2=240