Assume a population is normally distributed with population standard deviation o

Question

Assume a population is normally distributed with population standard deviation of 100. Given a sample size of 64. with sample mean of 450. we perform the following hypothesis test. H_0: mu = 475 H_: mu notequalto 475 (a) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value? Why? (b) What is the test statistic? (Show work and round the answer to three decimal places) (c) 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) (d) What is your conclusion of the test at the alpha = 0.01 level? Why? (Show work)

Explanation / Answer

given mean =450

x^=475

n=64

df=64-1=63

SD=100

A)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 < 100
:
we use the standard error of the mean to calculate the test statistic
:
sample size is 64, the square root of 64 = 8 then
:
standard error of the mean = 100 / 8 = 12.5

b)test statistic is z = (475 - 450) / 12.5 = 2.000

significance level is 0.01 and we use the absolute value of the z-score

c)The p-value associated with 2.00 is 1 - 0.9772= 0.0228 rounding to three decimals 0.023

Since this is a two-tailed test we multiply by 2 = 2( 0.023)= 0.046 rounding to two decimal places = 0.05

d) Since 0.05 is greaters than 0.01, we fail to reject H_0

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