Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 14, 25, 17, 28, 15, 21. use table 2.a. calculate the sample mean and the sample standard deviation. (round intermediate calculations to 4 decimal places, "sample mean" to 3 decimal places and "sample standard deviation" to 2 decimal places.) sample mean sample standard deviation b. construct the 80% confidence interval for the population mean. (round "t" value to 3 decimal places, and final answers to 2 decimal places.) confidence interval to c. construct the 90% confidence interval for the population mean. (round "t" value to 3 decimal places, and final answers to 2 decimal places.) confidence interval to d. what happens to the margin of error as the confidence level increases from 80% to 90%? as the confidence level increases, the interval becomes narrower. as the confidence level increases, the interval becomes wider.

a:  Sample mean: 20, Sample standard deviation: 1.732

b:  19.13 <µ < 20.87

c:  18.84< µ < 21.16

d:  as the confidence level increases, the interval becomes wider

Step-by-step explanation:

a:  Sample mean is found by adding up all the individual values of the sample, then dividing by the total number of values in the sample.  

Sample standard deviation is the square root of the variance

See the first attached photo for the calculations of these values.

We need to create a 80% confidence interval for the population.  Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.  

Look for the column on the t-distribution chart that has "area in two tails" of 0.20 (80%), and row 7 (degree of freedom)

The t-value is 1.415

See the second attached photo for the construction of the confidence interval

We need to create a 90% confidence interval for the population.  Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.  

Look for the column on the t-distribution chart that has "area in two tails" of 0.10 (90%), and row 7 (degree of freedom)

The t-value is 1.895

See the third attached photo for the construction of the confidence interval

yess

step-by-step explanation:

idk whyy this is happening, i cant even read my notification bc i keep getting errors

~coco

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: