Styles pts) Assume a population is normally distributed with population standard
ID: 3307092 • Letter: S
Question
Styles pts) Assume a population is normally distributed with population standard deviation of 100. Given a sample size of 100, with sample mean of 500, we perform the following hypothesis test. Ho: = 525 Ha: 525 (a) (2 pts) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value? Why? (b) (4 pts) What is the test statistic? (Show work and round the answer to three decimal places) (c) (4 pts) What is the p-value? (Show work and round the answer to three decimal places. If you use technology to find the P-value, you have to describe the steps) (d) (2 pts) what is your conclusion of the test at the =0.05 level? Why? (Show 1vork)Explanation / Answer
a) from hypothesis; this is a test for population mean.
as we know the population std deviation ; we will apply z test (normal distribution)
b) from above std error of mean =std deviation/(n)1/2 =100/(100)1/2 =10
therefore test stat z =(X-mean)/std error =(500-525)/10 =-2.5
c) for above test stat ; p value =0.0124
d) for p value is lower then 0.05 level of signifcance therefore we reject nulll hypothesis
we have sufficient evidence at 0.05 level to conclude that population mean is different from 525.