Decide whether each point is a solution to the system. y≤3x+4 and y <3x-2
1 answer:
All the points are the solution of the given inequalities except y < 3x-2 at ( 3, 13).
<h3>What is inequality?</h3>inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
We will check all the points for the given inequality as follows:-
Point Y ≤ 3x - 2 y ≤ 3x + 4
( 0,-2) -2 ≤ 3 ( 0) -2 -2 ≤ 0+4
-2 ≤ -2 -2 ≤ 4
Correct Correct
( 5, 0 ) 0 ≤ ( 5 x3 ) -2 0 ≤ ( 5 x 3 ) + 4
0 ≤ 13 0 ≤ 19
Correct Correct
( 3, 13 ) 13 ≤ ( 3 x 3 ) -2 13 ≤ ( 3x3) + 4
13 ≤ 7 13 ≤ 13
Incorrect Correct
As we can see the given points satisfy all the given inequalities but points ( 3, 13 ) are not satisfying the inequality y ≤ 3x - 2 it is giving 13 ≤ 7 here 13 is not less than 7.
Therefore the points are the solution of the given inequalities except for y < 3x-2 at ( 3, 13).
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Answer:
Part a
We need to conduct a one tailed test
We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Part b: Calculate the statistic
We can replace in formula (1) the info given like this:
Part c :P-value
Since is a one sided test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.
Step-by-step explanation:
a. Should the alternative hypothesis be one-sided or two-sided?
b. Test the hypothesis that the mean adhesion is 2.5 dyne-cm².
c. What is the P-value of the test statistic?
Data given and notation
Data: 2.69, 5.76, 2.67, 1.62 ,4.12
We can calculate the sample mean with this formula:
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.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
Part a: State the null and alternative hypotheses.
We need to conduct a one tailed test
We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Part b: Calculate the statistic
We can replace in formula (1) the info given like this:
Part c :P-value
Since is a one sided test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.