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 = 4.45.
Compute the value of the test statistic. (Round your answer to three decimal places.)
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 < 0.025
p-value < 0.010
At α = 0.05, what is your conclusion?
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.
Do not reject H0. There is sufficient evidence to conclude that μ > 12.
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?
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.
Do not reject H0. There is sufficient evidence to conclude that μ > 12.
Test statistics
The value of the test statistic is 2.247
Degrees of Freedom df = n-1 = 25-1 = 24
P-value corresponding to t = 2.247 and df = 24 for a right tailed test is obtained using p-value calculator. Screenshot below:
P-value = 0.0171
Thus, correct answer is: .010 < p-value < 0.025
Since p-value = 0.0171 < α = 0.05, we reject null hypothesis H0. There is sufficient evidence to conclude that μ > 12.
Critical t value corresponding to df = 24 and α = 0.05 for a right-tailed test is obtained using critical t value calculator. screenshot below:
Critical t-value = 1.711
Since it is a right tailed test so rejection region is
test statistic ≤ NONE
test statistic ≥ 1.711
In this case test statistic = 2.247 ≥ Critical t value = 1.711, so we reject H0. There is sufficient evidence to conclude that μ > 12.