Question

The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 350 ​pounds, the​ company's safety inspectors have set a standard of ensuring that the stand can support an average of over 575 pounds. Their inspectors regularly subject a random sample of the stands to increasing weight until they fail. They test the hypothesis Upper H 0​: muequals575 against Upper H Subscript Upper A​: mugreater than575​, using the level of significance alphaequals0.01. If the sample of stands fails to pass this safety​ test, the inspectors will not certify the product for sale to the general public. The manufacturer is thinking of revising its safety test. Complete parts a through c below.

a) is this an upper-tail or lower tall test? In the context off the problem, Why is this important
This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily.
This is a lower-tail test because the weight of the TV sets must be less than the strength of the stands.
This is an upper-tail test because the TV sets will be placed on top of the stands.
This is a lower-tail test because the company tests the strength of the stands by starting with a weight below the desired strength and gradual increasing it.

b) Explain what will happen if the inspectors commit a Type l error. Choose the correct answer below.
They will decide the stands are safe when they're not.
They will decide the stands will hold 350 pounds easily when in fact the stands can hold 525 pounds easily.
They will decide the stands will hold 525 pounds easily when in fact the stands can only hold 350 pounds easily.
They will decide the stands are unsafe when they are in fact safe.

c) Explain what will happen if the inspectors commit a Type II error. Choose the correct answer below.
They will decide the stands are unsafe when they are in fact safe.
They will decide the stands will hold 350 pounds easily when in fact the stands can hold 525 pounds easily.
They will decide the stands will hold 525 pounds easily when in fact the stands can only hold 350 pounds easily.
They will decide the stands are safe when they're not.

Answer 1

a) "This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b) "They will decide the stands are safe when they're not."

c) "They will decide the stands are unsafe when they are in fact safe."

Explanation:

a) As the alternative hypothesis Ha is μ>575, the rejection region lays in the upper tail. Then, it is an upper-tail test.

They are testing the claim that the stand supports an average of 575 pounds or more, and are looking for statistical evidence for that claim.

"This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b) A Type I error happens when a true null hypothesis is rejected.

This would mean that a stands that doesn't really hold 575 pounds or more has passed the test. The stand would appear more safe than it is.

"They will decide the stands are safe when they're not."

c) A Type II error happens when a false null hypothesis failed to be rejected. In this case, a safe stand, that suports 575 pounds or more, does not pass the test.

"They will decide the stands are unsafe when they are in fact safe."