SOLUTION: Please help me with this: Assume the population is normally distributed. Given a sample size of 225, with sample mean of 750 and standard deviation of 30, we perform the follow

Question 1051028: Please help me with this:
Assume the population is normally distributed. Given a sample size of 225, with sample mean of 750 and standard deviation of 30, we perform the following hypothesis test.
H_0: μ=745
H_a: μ≠745
Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

What is the test statistic? (Show work and round the answer to three decimal places)

What is the p-value? (Show work and round the answer to two decimal places. If you use technology to find the P-value, you have to describe the steps)

What is your conclusion of the test at the α = 0.1005 level? Why? (Show work)
I appreciate your time, thank you!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Because H_a contains not equal, we use a two-tailed test
:
The test is for population mean and we can use the Normal distribution since
we are given that the population is normally distributed and the sample size is > 30
:
we use the standard error of the mean to calculate the test statistic
:
sample size is 225, the square root of 225 = 15, then
:
standard error of the mean = 30 / 15 = 2
:
**********************************************
test statistic is z = (745 - 750) / 2 = -2.500
**********************************************
:
significance level is 0.1005 and we use the absolute value of the z-score
:
The p-value associated with 2.500 is 1 - 0.9938 = 0.0062
:
**************************************************************************
Since this is a two-tailed test we multiply by 2 = 0.0124 2-tailed p-value
**************************************************************************
:
***********************************************
Since 0.0125 is less than 0.1005, we reject H_0
***********************************************
:

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