Please Show all work( Equations and etc) (PRACTICE Problem) Section 92, Problem

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Please Show all work( Equations and etc)

(PRACTICE Problem) Section 92, Problem 1: A random sample of n-36 observations from a population with mean and variance o2, where 2- 0.25, produced a sample mean X = 4.2 and a sample standard deviation equal to 0.5. If it is desired to test that the population mean exceeds 4.0, describe the null hypothesis and alternative hypothesis and carry out the testing of hypothesis at the 5% level of significance Null hypothesis: Ho Alternative hypothesis: H1: Critical point, a, for = 0.05 Observed Z-statistic: Z Accept or Reject Ho:

Explanation / Answer

SECTION 9.2 PROBLEM 1:
Given that,
population mean(u)=4
standard deviation, =0.5
sample mean, x =4.2
number (n)=36
null, Ho: =4
alternate, H1: >4
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 4.2-4/(0.5/sqrt(36)
zo = 2.4
| zo | = 2.4
critical value
the value of |z | at los 5% is 1.645
we got |zo| =2.4 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 2.4 ) = 0.01
hence value of p0.05 > 0.01, here we reject Ho
ANSWERS
---------------
null, Ho: =4
alternate, H1: >4
test statistic: 2.4
critical value: 1.645
decision: reject Ho
p-value: 0.01

hence we have evidence that population mean exceeds 4.0

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