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lilly4920
12.02.2020 •
Mathematics
State the null an alternative hypothesis in the following situations by defining the parameters used. Also, state any assumptions that you need to make to conduct the test: (a) The postal service wishes to prove that the mean delivery time for packages is less than 5 days. (b) A financial institution believes that it has an average loan processing time of less than 10 days. (c) A marketing firm believes that the average contract for a customer exceeds $50,000. (d) A Web-order company wished to test if it has improved its efficiency of operations by reducing its average response time. (e) A manufacturer of consumer durables believes that over 70% of its customers are satisfied with the product.
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Ответ:
a) Let X the random variable who represent the mean delivery time for packages. They want to test if this time is lss than 5 days (alternative hypothesis) so we have:
Null hypothesis:![\mu_X \geq 5](/tpl/images/0507/4936/62689.png)
Alternative hypothesis:![\mu_X < 5](/tpl/images/0507/4936/b57b5.png)
b) Let X the random variable who represent the loan processing time. They want to test if this time is less than 10 days (alternative hypothesis) so we have:
Null hypothesis:![\mu_X \geq 10](/tpl/images/0507/4936/2d393.png)
Alternative hypothesis:![\mu_X < 10](/tpl/images/0507/4936/95a06.png)
c) Let X the random variable who represent the amoutn of money for the contract of a customer. They want to test if this amount exceeds 50000$ (alternative hypothesis) so we have:
Null hypothesis:![\mu_X \leq 50000](/tpl/images/0507/4936/c3b7d.png)
Alternative hypothesis:![\mu_X 50000](/tpl/images/0507/4936/f0caf.png)
d) Let's assume that the average response time is
and X represent the variable the response time, so we want to check this:
Null hypothesis:![\mu_X \geq \mu_o](/tpl/images/0507/4936/6d107.png)
Alternative hypothesis:![\mu_X < \mu_o](/tpl/images/0507/4936/0649e.png)
e)For this case we are interested on the proportion of customers satisfied with a product and we want to test if this proportion is higher than 0.7 or 70% so the system of hypothesis should be:
Null hypothesis:![p \leq 0.7](/tpl/images/0507/4936/78ce2.png)
Alternative hypothesis:![p0.7](/tpl/images/0507/4936/c3292.png)
Step-by-step explanation:
Part a
Let X the random variable who represent the mean delivery time for packages. They want to test if this time is less than 5 days (alternative hypothesis) so we have:
Null hypothesis:![\mu_X \geq 5](/tpl/images/0507/4936/62689.png)
Alternative hypothesis:![\mu_X < 5](/tpl/images/0507/4936/b57b5.png)
Part b
Let X the random variable who represent the loan processing time. They want to test if this time is less than 10 days (alternative hypothesis) so we have:
Null hypothesis:![\mu_X \geq 10](/tpl/images/0507/4936/2d393.png)
Alternative hypothesis:![\mu_X < 10](/tpl/images/0507/4936/95a06.png)
Part c
Let X the random variable who represent the amoutn of money for the contract of a customer. They want to test if this amount exceeds 50000$ (alternative hypothesis) so we have:
Null hypothesis:![\mu_X \leq 50000](/tpl/images/0507/4936/c3b7d.png)
Alternative hypothesis:![\mu_X 50000](/tpl/images/0507/4936/f0caf.png)
Part d
Let's assume that the average response time is
and X represent the variable the response time, so we want to check this:
Null hypothesis:![\mu_X \geq \mu_o](/tpl/images/0507/4936/e2771.png)
Alternative hypothesis:![\mu_X < \mu_o](/tpl/images/0507/4936/0649e.png)
Part e
For this case we are interested on the proportion of customers satisfied with a product and we want to test if this proportion is higher than 0.7 or 70% so the system of hypothesis should be:
Null hypothesis:![p \leq 0.7](/tpl/images/0507/4936/78ce2.png)
Alternative hypothesis:![p0.7](/tpl/images/0507/4936/c3292.png)
Ответ:
-6
Step-by-step explanation:
The average rate of change is given by
f(x2) - f(x1)
x2-x1
x2=5 and x1 = 1
f(5) =7 - 5^2 = 7-25 = -18
f(1) = 7-1^2 = 7-1 = 6
-18-6
5-1
-24
4
-6