The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. she would now like to determine whether or not the mean age of her customers is greater than 30. if so, she plans to alter the entertainment to appeal to an older crowd. if not, no entertainment changes will be made. if she wants to have a level of significance at 0.01, what rejection region should she use?
1. reject h0 if t < -2.3263.
2. reject h0 if t > 2.3263.
3. reject h0 if t < -2.5758.
4. reject h0 if t > 2.5758.

Option 2.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 30

Sample size, n = 250

Alpha, α = 0.01

First, we design the null and the alternate hypothesis

We use Right-tailed t test to perform this hypothesis.

Formula:

Now,

Decision rule:

For a right ailed t-test,

, we reject the null hypothesis as it lies in the rejection area.

, we fail to reject the null hypothesis as it lies in the acceptance area and accept the null hypothesis.

Thus,

Option 2.

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