Zappos is an online retailer based in Nevada and employs 1,300 employees. One of their competitors, Amazon, would like to test t
1 answer:
Answer:
Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old
Step-by-step explanation:
Data given
represent the sample mean
represent the sample 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)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 36 years old, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
And replacing we got:
Now we can calculate the critical value but first we need to find the degreed of freedom:
So we need to find a critical value in the t distribution with df =21 who accumulates 0.025 of the area in the left and we got:
Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old
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Solution :
Let and
represents the proportions of the seeds which germinate among the seeds planted in the soil containing
and
mushroom compost by weight respectively.
To test the null hypothesis against the alternate hypothesis
.
Let denotes the respective sample proportions and the
represents the sample size respectively.
The test statistic can be written as :
which under follows the standard normal distribution.
We reject at
level of significance, if the P-value
or if
Now, the value of the test statistics = -1.368928
The critical value =
P-value =
= 0.171335
Since the p-value > 0.05 and , so we fail to reject
at
level of significance.
Hence we conclude that the two population proportion are not significantly different.
Conclusion :
There is not sufficient evidence to conclude that the of the seeds that
with the percent of the
in the soil.
Answer:
a. Line
b. Plane
c. All of R^3
Step-by-step explanation:
In order to answer this question, we need to study the linear independence between the vectors :
1 - A set of three linearly independent vectors in R^3 generates R^3.
2 - A set of two linearly independent vectors in R^3 generates a plane.
3 - A set of one vector in R^3 generates a line.
The next step to answer this question is to analyze the independence between the vectors of each set. We can do this by putting the vectors into the row of a R^(3x3) matrix. Then, by working out with the matrix we will find how many linearly independent vectors the set has :
a. Let's put the vectors into the rows of a matrix :
⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒
We find that the second vector is a linear combination from the first and the third one (in fact, the second vector is the first vector multiply by -3).
We also find that the third vector is a linear combination from the first and the second one (in fact, the third vector is the first vector multiply by 5).
At the end, we only have one vector in R^3 ⇒ The set of all linear combinations of the set a. is a line in R^3.
b. Again, let's put the vectors into the rows of a matrix :
⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒
We find that there are only two linearly independent vectors in the set so the set of all linear combinations of the set b. is a plane (in fact, the third vector is equivalent to the first vector plus three times the second vector).
c. Finally :
⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒
The set is linearly independent so the set of all linear combination of the set c. is all of R^3.