In: Statistics and Probability
Consider the following hypothesis test.
H0: μ ≤ 12
Ha: μ > 12
A sample of 25 provided a sample mean
x = 14
and a sample standard deviation
s = 4.57.
(a)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(b)
Use the t distribution table to compute a range for the p-value.
p-value > 0.2000.100 < p-value < 0.200 0.050 < p-value < 0.1000.025 < p-value < 0.0500.010 < p-value < 0.025p-value < 0.010
(c)
At
α = 0.05,
what is your conclusion?
Do not reject H0. There is sufficient evidence to conclude that μ > 12.Do not reject H0. There is insufficient evidence to conclude that μ > 12. Reject H0. There is insufficient evidence to conclude that μ > 12.Reject H0. There is sufficient evidence to conclude that μ > 12.
(d)
What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer to three decimal places.)
test statistic≤test statistic≥
What is your conclusion?
Do not reject H0. There is sufficient evidence to conclude that μ > 12.Do not reject H0. There is insufficient evidence to conclude that μ > 12. Reject H0. There is insufficient evidence to conclude that μ > 12.Reject H0. There is sufficient evidence to conclude that μ > 12.
Solution :
= 12
= 14
s = 4.57
n = 25
df = n-1 = 25-1 = 24
This is the right tailed test .
The null and alternative hypothesis is
H0 : ≤ 12
Ha : > 12
a) Test statistic = t
= ( - ) / s / n
= (14-12) / 4.57 / 25
= 2.188
b) p(Z >2.18 ) = 1-P (Z <2.18 ) = 0.0193
P-value = 0.0193
= 0.05
p=0.0193<0.05
c) Reject H0. There is sufficient evidence to conclude that μ > 12.
d) = 0.05
The critical value for a right-tailed test is tc=1.711.
The rejection region t >1.711
Reject H0. There is sufficient evidence to conclude that μ > 12.