Identify the critical t. An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t value t∗t∗ for the given sample size and confidence level. Round critical t values to 3 decimal places. Sample size, n Confidence level Degree of Freedom Critical value, t∗t∗5 90 13 95 22 98 15 99

Answer and Step-by-step explanation: The critical value for a desired confidence level is the distance where you must go above and below the center of distribution to obtain an area of the desired level.

Each sample has a different degree of freedom and critical value.

To determine critical value:

1) Calculate degree of freedom: df = n - 1

2) Subtract the level per 100%;

3) Divide the result by 2 tails;

4) Use calculator or table to find the critical value t*;

For n = 5 Level = 90%:

df = 4

t = = 0.05

Using t-table:

t* = 2.132

n = 13 Level = 95%:

df = 12

t = = 0.025

Then:

t* = 2.160

n = 22 Level = 98%

df = 21

t = = 0.01

t* = 2.819

n = 15 Level = 99%

df = 14

t = = 0.005

t* = 2.977

The critical values and degree of freedom are:

sample size          level           df              critical value

     5                      90%           4                   2.132

   13                       95%            12                 2.160

   22                      98%            21                 2.819

   15                       99%            14                 2.977

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction