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.

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

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:

Alternative hypothesis:

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

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step-by-step explanation: