Question

Given the following hypotheses: H0: μ ≤ 11 H1: μ > 11 A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 5.0. Using the 0.025 significance level:

a. State the decision rule. (Round your answer to 3 decimal places.)

Answer 1

n = 10

sample mean = 12

sample sd = 5

Assuming that the data is normally distributed and also as the sample size is less than 30 we will use t stat.

Decision rule:

df = 9

level of significance = 0.025

right tailed test

t critical = 2.262

If the t stat is greater than t critical (2.262) , we will reject the Null hypothesis.

IF the t stat is less than t critical (2.262), we fail to reject the NUll hypothesis.

Here, t stat (0.632) is less than t critical (2.262) hence we fail to reject the Null hypothesis.