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

is means division by fractions

step-by-step explanation:

x=half

step-by-step explanation: