Question

The proportion of residents in Phoenix favoring the building of
toll roads to complete the freeway system is believed to be
*p* = 0.3. If a random sample of 15 residents shows that one
or fewer favor this proposal, we will conclude that *p* <
0.3.

- Find the probability of type I error if the true proportion is
*p*= 0.3. - Find the probability of committing a type II error with this
procedure if
*p*= 0.2. - What is the power of this procedure if the true proportion is
*p*= 0.2?

Answer #1

1.
A) The proportion of residents in Phoenix favoring the building
of toll roads to complete the freeway system is believed to be
p=0.3. If a random sample of 100 individuals shows that 25 favor
building toll roads do we have evidence at the 5% level to claim
the true proportion is really lower?
B) A manufacturer produces crankshafts for an automobile engine.
The crankshaft's diameter (3cm) is of interest because it is likely
to have an impact on warranty...

A fabric manufacturer believes that the proportion of orders for
raw material arriving late isp= 0.6. If a random sample of 10
orders shows that 4 or fewer arrived late, the hypothesis thatp=
0.6should be rejected in favor of the alternativep <0.6. (a)Find
the probability of committing a type II error for the
alternativesp= 0.5 (b)Find the probability of committing a type I
error if the true proportion isp= 0.6.

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