In a survey, people were asked whether they thought sun went around the planet Earth or vice versa. Of 1910 people, 241 thought the sun went around Earth. a. What proportion of people in the survey believed the sun went around Earth? b. Find a 95% confidence interval for the proportion of all people with this belief. c. Suppose a scientist said that 20% of people in the general population believe the sun goes around Earth. Using the confidence interval, would you say that was plausible? Explain your answer. a. The proportion of people in the survey who believed the sun went around Earth is . 126. (Round to three decimal places as needed.) b. The 95% confidence interval is (nothing comma nothing ). (Round to three decimal places as needed.) c. Is the scientist's claim that 20% of people in the general population believe the sun goes around Earth plausible? No, it is not plausible, since the value . 126 is not inside of the confidence interval. (Type an integer or a decimal. Do not round.)

a) 0.1203

b) The 95% confidence interval for the proportion of all people with this belief is (0.1057, 0.1349).

c) 20% is not plausible, since it is not part of the confidence interval.

Step-by-step explanation:

We have that:

1920 asked if the sun went around the planet Earth or vice versa.

241 thought the sun went around Earth.

a. What proportion of people in the survey believed the sun went around Earth?

b. Find a 95% confidence interval for the proportion of all people with this belief.

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 95% confidence interval for the proportion of all people with this belief is (0.1057, 0.1349).

c. Suppose a scientist said that 20% of people in the general population believe the sun goes around Earth. Using the confidence interval, would you say that was plausible? Explain your answer.

We are 95% sure that the true proportion of the general population who believe the sun goes around Earth is between (0.1057, 0.1349)

So 20% is not plausible, since it is not part of the confidence interval.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3