Question

Consider the follovwing hypothesis test. Ho: us 12 H:u > 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.33. (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. O p-value > 0.200 0.100 < p-value < 0.200 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 O p-value < 0.010 (c) At a = 0.05, what is your conclusion? O Do not reject H. There is sufficient evidence to conclude that u > 12. O Reject Ho There is sufficient evidence to conclude that u > 12. Reject H. There is insufficient evidence to conclude that u > 12. Do not reject H. There is insufficient evidence to conclude that u > 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 s test statistic 2 What is your conclusion? Do not reject H. There is sufficient evidence to conclude that u > 12. Reject Ho. There is sufficient evidence to conclude that u > 12. Reject H.. There is insufficient evidence to conclude that u > 12. o' O Do not reject H. There is insufficient evidence to conclude that u > 12.

Answer 1

a)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (14 - 12)/(4.33/sqrt(25))
t = 2.309

b)

P-value Approach
P-value = 0.0149

0.010 < p value < 0.025

c)

As P-value < 0.05, reject the null hypothesis.

Reject H0. There is sufficient evidence to conclude that mu > 12

d)

test statistic < = NONE
test statistic >= 1.711

Reject H0. There is sufficient evidence to conclude that mu > 12