Brainliest + 20 pts to whoever helps pls!!

Eighty-one random people were surveyed about the time it takes to commute to work in the morning. The standard deviation of the simple random sample is 2.3 minutes. The test statistic for the sample is 105.8. Find the critical values, using a significance level of 0.10, needed to test a claim that the standard deviation of all commute times is equal to 2.0 minutes. State the initial conclusion.
a. 60.391 and 101.879; because the test statistic is in a critical region, the test rejects the null hypothesis.
b. 60.391 and 101.879; because the test statistic is outside of the critical region, the test fails to reject the null hypothesis.
c. 69.126 and 113.145; because the test statistic is in a critical region, the test rejects the null hypothesis.
d. 69.126 and 113.145; because the test statistic is in the critical region, the test fails to reject the null hypothesis.

Correct option is (a). 60.391 and 101.879; because the test statistic is in a critical region, the test rejects the null hypothesis.

Step-by-step explanation:

A Chi-square test for population variance is used to perform this test.

The standard deviation is, 2.0 minutes.

Then the variance is, 4.0 minutes.

The hypothesis for this test is:

H₀: The population variance of all commute times is equal to 4.0 minutes, i.e. σ² = 4.

Hₐ: The population variance of all commute times is not equal to 4.0 minutes, i.e. σ² ≠ 4.

The test statistic is:

The critical region of this test is defined as:

Reject H₀ if or .

The degrees of freedom is:

Compute the critical from a Chi-square table.

The test statistic value is, .

The null hypothesis is rejected because the test statistic is in the critical region.

Thus, the correct option is (a).

step-by-step explanation:

what grade level is this? need to know so i can look in my old textbooks!

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is