Answer:
There is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.
Step-by-step explanation:
We have to answer the population proportion for Vermont.
We can only do it by a confidence interval, as we only have information from a sample.
This sample, of size n=100, has a proportion p=0.653.
The degrees of freedom are:
![df=n-1=100-1=99](https://tex.z-dn.net/?f=df%3Dn-1%3D100-1%3D99)
We will calculate a 95% confidence interval, which for df=99 has a critical value of t of t=1.984.
The margin of error can be calculated as:
![E=t*\sigma_p=t\sqrt{\dfrac{p(1-p)}{n}}=1.984\sqrt{\dfrac{0.653*0.347}{100}}\\\\\\E=1.984*\sqrt{0.00226}=1.984*0.0476=0.094](https://tex.z-dn.net/?f=E%3Dt%2A%5Csigma_p%3Dt%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%3D1.984%5Csqrt%7B%5Cdfrac%7B0.653%2A0.347%7D%7B100%7D%7D%5C%5C%5C%5C%5C%5CE%3D1.984%2A%5Csqrt%7B0.00226%7D%3D1.984%2A0.0476%3D0.094)
Then, the upper and lower bounds of the confidence interval are:
![LL=p-E=0.653-0.094=0.559\\\\UL=p+E=0.653+0.094=0.747](https://tex.z-dn.net/?f=LL%3Dp-E%3D0.653-0.094%3D0.559%5C%5C%5C%5CUL%3Dp%2BE%3D0.653%2B0.094%3D0.747)
Then, we can say that there is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.
Answer:
The answer is D!
Step-by-step explanation: Type equations into y= and see what happens.
The domain is the start and end of the graph. so in this case the function starts at -2 and ends at -4 so (C.) would be your answer.
Answer:
x = 3 or y = 1
Step-by-step explanation:
The line with the equation y = x + 2 passes through the point (1,3), because the coordinates of this point satisfy the equation (
).
Line y = x + 2 has the slope m = 1, that means the angle between this line and positive direction of x-axis is 45°.
Thus, the line which form the angle from the line with equation y=x+2 of 45° is the vertical or horizontal line.
Vertical line has the equation x = 1, horizontal line has the equation y = 3.