Assume that both populations are normally distributed. a) Test whether mu 1 not equals mu 2 at the alpha equals 0.05 level of significance for the given sample data. b) Construct a 95% confidence interval about mu 1 minus mu 2. Sample 1 Sample 2 n 19 19 x overbar 16.2 14.1 s 4.5 3.1

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

sample size 1

sample size 2

sample mean for group 1

sample mean for group 2

sample deviation for group 1

sample deviation for group 2

Solution to the problem

For this case the confidence interval is given by:

And the degrees of freedom are given by:

We want a 95% of confidence o then the significance level is 1-0.95 =0.05 and if we find a critical value in the t distribution with 36 degrees of freedom we got:

And replacing we got:

(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

d. vertex

step-by-step explanation: