Question

Given the following hypotheses: Hy: 13 Hu> 13 A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 4.3. Using the 0.1 significance level: a. State the decision rule. (Round your answer to 3 decimal places.) Reject HO ift b. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic

Answer 1

Part a

We are given

α = 0.1

Test is upper tailed or right tailed.

n = 10

df = n – 1 = 9

Critical value = 1.3830

Reject H0 if t > 1.383

Part b

Test statistic is given as below:

t = (Xbar - µ)/[S/Sqrt(n)]

t = (12 – 13)/[4.3/sqrt(10)]

t = -0.735

Value of the test statistic = -0.735

Part c

Do not reject H0. There is not sufficient evidence to conclude that the population mean is greater than 13.

[We do not reject H0 because test statistic t is not greater than 1.383. ]