Answer:
Part a
The test statistic and P-value of the test is 1.581 and 0.057.
Part b
The type-II error is 0.0088.
Part c
The power of the test is 0.9912.
Explanation:
The Z− test is a statistical test for the mean of a population. It can be used when
or when the population is normally distributed and population standard deviation
is known.
The type-II error is defined as the probability of accepting the null hypothesis when it is actually false. It is denoted by the Greek letter beta
.
The power of a test against a specific alternative is the probability that the test will reject
at a chosen significance level
when the specified alternative value of the parameter is true.
The formula for the Z− test is,
Here,
represents the sample mean
represents the population mean
represents the population standard deviation
represents the sample size
The formula for the type-II error is,

The formula for the power is,
Here,
represents the type-II error
a)
The sample size is
The population standard deviation is,
The sample average is
Null hypothesis
Calculate the test statistic value.

Calculate the P− value of the hypothesis test.

b)
Calculate the type-II error.

c)
Calculate the power of the test.