The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. x^^\_ +/-\(t text( critical value)\)s/sqrt(n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.) (a) 95% confidence, n = 17(b) 90% confidence, n = 12 (c) 99% confidence, n = 24 (d) 90% confidence, n = 24 (e) 80% confidence, n = 13 (f) 95% confidence, n = 10

a) 2.120

b) 1.796

c) 2.807

d) 1.714

e) 1.356

f) 2.262

Step-by-step explanation:

The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. x^^\_ +/-\(t text( critical value)\)s/sqrt(n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.)

(a) 95% confidence, n = 17

We find our degrees of freedom first

= n - 1

= 17 - 1

= 16

The t critical value using the t table =

2.120

(b) 90% confidence, n = 12

We find our degrees of freedom first

= n - 1

= 12 - 1

= 11

The t critical value using the t table =

1.796

(c) 99% confidence, n = 24

We find our degrees of freedom first

= n - 1

= 24 - 1

= 23

The t critical value using the t table = 2.807

(d) 90% confidence, n = 24

We find our degrees of freedom first

= n - 1

= 24 - 1

= 23

The t critical value using the t table =

1.714

(e) 80% confidence, n = 13

We find our degrees of freedom first

= n - 1

= 13- 1

= 12

The t critical value using the t table = 1.356

(f) 95% confidence, n = 10

We find our degrees of freedom first

= n - 1

= 10 - 1

= 9

The t critical value using the t table =

2.262

Part 1) The equation of the perpendicular bisector of the segment AB is

 or  

Part 2)

Part 3)

Step-by-step explanation:

step 1

Find the midpoint AB (because a bisector divide into two equal parts)

we have

A(3, 0) and B(–1, 2)

step 2

Find the slope AB

we have

A(3, 0) and B(–1, 2)

The formula to calculate the slope between two points is equal to

substitute the values

step 3

Find the slope of the perpendicular bisector of the segment AB

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product is equal to -1)

m1*m2=-1

we have

so

step 4

Find the equation of the perpendicular bisector of the segment AB

we have

-----> midpoint AB

substitute

Convert to slope intercept form

step 5

Find the x-intercept (point P)

For y=0

0=2x-1

2x=1

x=0.5

The x-intercept is the point P(0.5,0)

step 6

Find the length PA

we have

P(0.5,0),A(3,0)

the formula to calculate the distance between two points is equal to

substitute the values

step 7

Find the length PB

we have

P(0.5,0),B(-1,2)

the formula to calculate the distance between two points is equal to

substitute the values