Question

A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 25

H₁: μ > 25

1. Is this a one- or two-tailed test?

• "One-tailed"—the alternate hypothesis is greater than direction.

• "Two-tailed"—the alternate hypothesis is different from direction.

2. What is the decision rule? (Round your answer to 2 decimal places.)

3. What is the value of the test statistic? (Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject

• Do not reject

5. What is the p-value? (Round your answer to 4 decimal places.)

Answer 1

Given that,
population mean(u)=25
standard deviation, σ =4
sample mean, x =26
number (n)=35
null, Ho: μ<=25
alternate, H1: μ>25
level of significance, α = 0.05
from standard normal table,right tailed z α/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 = 26-25/(4/sqrt(35)
zo = 1.479
| zo | = 1.479
critical value
the value of |z α| at los 5% is 1.645
we got |zo| =1.479 & | z α | = 1.645
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value : right tail - ha : ( p > 1.479 ) = 0.07
hence value of p0.05 < 0.07, here we do not reject Ho
ANSWERS
---------------
a.
one tailed test
b.
null, Ho: μ<=25
alternate, H1: μ>25
c.
test statistic: 1.479
d.
critical value: 1.645
decision: do not reject Ho
e.
p-value: 0.07
f.
we do not have enough evidence to support the claim that population mean is greater than 25.