The average gasoline price of one of the major oil companies has been $2.20 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14. Assume that the standard deviation of the population (s) is $0.12. At 95% confidence, test the company's claim. The hypotheses are:H0: m 2.20Ha: m < 2.20If the test is done at 95% confidence, the null hypothesis should

Since is a one sided lower test the p value would be:  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 2.2$ per gallon

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the population standard deviation

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean for the prices is less than 2.20, the system of hypothesis are:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

P-value  

Since is a one sided lower test the p value would be:  

Conclusion  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 2.2$ per gallon

use formula for the circle a=3.14

step-by-step explanation:

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