A random sample of 500 registered voters in Phoenix is asked if they favor the use of oxygenated fuels year-round to reduce air pollution. If more than 313 voters respond positively, we will conclude that at least 60% of the voters favor the use of these fuels. Required:
a. Find the probability of type I error if exactly 60% of the voters favor the use of these fuels.
b. What is the type II error probability β if 75% of the voters favor this action?

Step-by-step explanation:

From the question we are told that:

Population size size

Sample mean

Null hypothesis

Alternative hypothesis

Generally the equation for for P value is mathematically given by

Generally the mean is mathematically given by

Generally the standard deviation is mathematically given by

a)

Generally the probability of Type_I error is mathematically given as

Therefore using z table

b)

Null hypothesis

Alternative hypothesis

Generally the probability of Type_II error is mathematically given as

Generally the mean is mathematically given by

Generally the standard deviation is mathematically given by

Therefore

Therefore from standard normal table

a negative exponent is translated as follows:

so, we have

it's both, now can you answer my most recent question?