Describe type I and type II errors for a hypothesis test of the indicated claim.   A lumber   store claims that at least   25 ​% of its new customers will return to buy their next order of lumber . Describe the type I error. Choose the correct answer below.     A. A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber   is at least   0.25 ​, but you reject Upper H 0 ​: pgreater than or equals 0.25 .   B. A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber   is no more than   0.25 ​, but you reject Upper H 0 ​: pless than or equals 0.25 .   C. A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber   is at least   0.25 ​, but you fail to reject Upper H 0 ​: pgreater than or equals 0.25 .   D. A type I error will occur when the actual proportion of new customers who return to buy their next order of lumber   is no more than   0.25 ​, but you fail to reject Upper H 0 ​: pless than or equals 0.25 . Describe the type II error. Choose the correct answer below.     A. A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber   is more than   0.25 ​, but you fail to reject Upper H 0 ​: pgreater than or equals 0.25 .   B. A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber   is less than   0.25 ​, but you fail to reject Upper H 0 ​: pgreater than or equals 0.25 .   C. A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber   is more than   0.25 ​, but you reject Upper H 0 ​: pless than or equals 0.25 .   D. A type II error will occur when the actual proportion of new customers who return to buy their next order of lumber   is less than   0.25 ​, but you reject Upper H 0 ​: pless than or equals 0.25.

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Describe type I and type II errors for a hypothesis test of the indicated claim.
 
A
lumber
 

store claims that

at least
 
25
​%

of its new customers will return to buy their next

order of lumber
.
Describe the type I error. Choose the correct answer below.
 
 
A.
A type I error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

at least
 
0.25
​,

but you reject

Upper H 0
​:
pgreater than or equals

0.25

.
 
B.
A type I error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

no more than
 
0.25
​,

but you reject

Upper H 0
​:
pless than or equals

0.25

.
 
C.
A type I error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

at least
 
0.25
​,

but you fail to reject

Upper H 0
​:
pgreater than or equals

0.25

.
 
D.
A type I error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

no more than
 
0.25
​,

but you fail to reject

Upper H 0
​:
pless than or equals

0.25

.
Describe the type II error. Choose the correct answer below.
 
 
A.
A type II error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

more than
 
0.25
​,

but you fail to reject

Upper H 0
​:
pgreater than or equals

0.25

.
 
B.
A type II error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

less than
 
0.25
​,

but you fail to reject

Upper H 0
​:
pgreater than or equals

0.25

.
 
C.
A type II error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

more than
 
0.25
​,

but you reject

Upper H 0
​:
pless than or equals

0.25

.
 
D.
A type II error will occur when the actual proportion of new customers who return to buy their next
order of lumber
 

is

less than
 
0.25
​,

but you reject

Upper H 0
​:
pless than or equals

0.25.

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