Question

Consider the following hypotheses: HO: 220 HA u < 220 A sample of 72 observations results in a sample mean of 209. The population standard deviation is known to be 18. (You may find it useful to reference the appropriate table: z table or tablet a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic

Answer 1

Given that,
population mean(u)=220
standard deviation, σ =18
sample mean, x =209
number (n)=72
null, Ho: μ>=220
alternate, H1: μ<220
level of significance, α = 0.1
from standard normal table,left tailed z α/2 =1.282
since our test is left-tailed
reject Ho, if zo < -1.282
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 209-220/(18/sqrt(72)
zo = -5.185
| zo | = 5.185
critical value
the value of |z α| at los 10% is 1.282
we got |zo| =5.185 & | z α | = 1.282
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : left tail - ha : ( p < -5.185 ) = 0
hence value of p0.1 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: μ>=220
alternate, H1: μ<220
a-1.
test statistic: -5.185
critical value: -1.282
decision: reject Ho
a-2.
p-value: 0
b.
yes,
p value is less than alpha value
we have enough evidence to support the claim that population mean is less than 220.
c.
Given that,
population mean(u)=220
standard deviation, σ =18
sample mean, x =209
number (n)=72
null, Ho: μ>=220
alternate, H1: μ<220
level of significance, α = 0.01
from standard normal table,left tailed z α/2 =2.326
since our test is left-tailed
reject Ho, if zo < -2.326
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 209-220/(18/sqrt(72)
zo = -5.185
| zo | = 5.185
critical value
the value of |z α| at los 1% is 2.326
we got |zo| =5.185 & | z α | = 2.326
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : left tail - ha : ( p < -5.185 ) = 0
hence value of p0.01 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: μ>=220
alternate, H1: μ<220
test statistic: -5.185
critical value: -2.326
decision: reject Ho
p-value: 0
yes,
p value is less than alpha value
d.
we have enough evidence to support the claim that population mean is less than 220.