Answer: β ≠ ±1
Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,
det ≠ 0
Determinant of a 3x3 matrix is calculated by:
det
β ≠ ±1
For the system to have only one solution, β ≠ 1 or β ≠ -1.
Answer:
I hope it will help you.......
Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c)
d) If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of men that write with their left hand is NOT significant lower than the proportion of female that write with their left hand
Step-by-step explanation:
1) Data given and notation
represent the number of men that write with their left hand
represent the number of women that write with their left hand
sample of male selected
sample of female selected
represent the proportion of men that write with their left hand
represent the proportion of women that write with their left hand
represent the significance level
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the rate of left-handedness among males is less than that among females , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
3) Calculate the statistic
Replacing in formula (1) the values obtained we got this:
4) Statistical decision
We have a significance level provided , and now we can calculate the p value for this test.
Since is a one left side test the p value would be:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of men that write with their left hand is NOT significant loer than the proportion of female that write with their left hand .