The tiger could polish off everything on that list in no time.
It would take him zero days to eat all of it, because all the prey
that you have listed adds up to zero pounds of meat.
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (-2, -2) and (-4, 1). Substitute:
![m=\dfrac{1-(-2)}{-4-(-2)}=\dfrac{1+2}{-4+2}=\dfrac{3}{-2}=-\dfrac{3}{2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B1-%28-2%29%7D%7B-4-%28-2%29%7D%3D%5Cdfrac%7B1%2B2%7D%7B-4%2B2%7D%3D%5Cdfrac%7B3%7D%7B-2%7D%3D-%5Cdfrac%7B3%7D%7B2%7D)
<h3>Answer: slope =
![-\dfrac{3}{2}](https://tex.z-dn.net/?f=-%5Cdfrac%7B3%7D%7B2%7D)
</h3>
Answer with explanation:
Let p be the population proportion.
Given : The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players.
i.e. ![p=\dfrac{5000}{20000}=0.25](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7B5000%7D%7B20000%7D%3D0.25)
![H_0:p\leq0.25\\\\H_a:p>0.25](https://tex.z-dn.net/?f=H_0%3Ap%5Cleq0.25%5C%5C%5C%5CH_a%3Ap%3E0.25)
Since alternative hypothesis is right-tailed , so the test is right-tailed test.
Also, Sample size : n= 300 ,
Sample proportion: ![\hat{p}=\dfrac{96}{300}=0.32](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B96%7D%7B300%7D%3D0.32)
Test statistic: ![z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D)
![z=\dfrac{0.32-0.25}{\sqrt{\dfrac{0.25(1-0.25)}{300}}}=2.8](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.32-0.25%7D%7B%5Csqrt%7B%5Cdfrac%7B0.25%281-0.25%29%7D%7B300%7D%7D%7D%3D2.8)
i.e. Observed test statistic Value = 2.80
(A) is right option.
Critical value for 5% significance level for right tailed test :-
![z_{\alpha}=z_{0.05}= 1.6448536](https://tex.z-dn.net/?f=z_%7B%5Calpha%7D%3Dz_%7B0.05%7D%3D%201.6448536)
Since , the observed z-value is greater than the critical value , so we reject the null hypothesis.
Conclusion : We have sufficient evidence to supposrt the alternative hypothesis.
So, The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with Blu-ray players.