What is the mean price for the sneakers?
1 answer:
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Answer:
1) For this case we want to check if the population deviation is less than 15( alternative hypothesis) and the system of hypothesis are:
H0:
H1:
B. H0:σ≥15, H1:σ<15
2) For this case we want to check if the population mean is at most 70000 (alternative hypothesis) and the system of hypothesis are:
H0:
H1:
C. H0:µ≥70,000, H1:µ<70,000
3) For this case we want to check if the population proportion of all internet users that make online purchases is higher than 0.5 (alternative hypothesis) and the system of hypothesis are:
H0:
H1:
D. H0:p≤0.5, H1:p>0.5
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Solution to the problem
1) For this case we want to check if the population deviation is less than 15( alternative hypothesis) and the system of hypothesis are:
H0:
H1:
B. H0:σ≥15, H1:σ<15
2) For this case we want to check if the population mean is at most 70000 (alternative hypothesis) and the system of hypothesis are:
H0:
H1:
C. H0:µ≥70,000, H1:µ<70,000
3) For this case we want to check if the population proportion of all internet users that make online purchases is higher than 0.5 (alternative hypothesis) and the system of hypothesis are:
H0:
H1:
D. H0:p≤0.5, H1:p>0.5
Answer: Yes, the given set of vectors is a basis of R³.
Step-by-step explanation: We are given to determine whether the following set of three vectors in R³ is a basis of R³ or not :
B = {(-1, 1,-1), (1, 0, 2), (1, 1, 0)} .
For a set to be a basis of R³, the following two conditions must be fulfilled :
(i) The set should contain three vectors, equal to the dimension of R³
and
(ii) the three vectors must be linearly independent.
The first condition is already fulfilled since we have three vectors in set B.
Now, to check the independence, we will find the determinant formed by theses three vectors as rows.
If the value of the determinant is non zero, then the vectors are linearly independent.
The value of the determinant can be found as follows :
Therefore, the determinant is not equal to 0 and so the given set of vectors is linearly independent.
Thus, the given set is a basis of R³.