Assume that a sample of 11 observations is drawn from a normally distributed population. The sample mean is 20 and the sample standard deviation is 5. Test the hypothesis is that population mean is greater than 18 at =5% significant level.

1. At 5% significant level with n-1 degree of freedom (11-1), the t-distributions critical value is 1.812 and the test t statistics is equal to 1.33 and therefore, I accept the null hypothesis.
2. At 5% significant level with n-1 degree of freedom (11-1), the t-distributions critical value is 1.812 and the test t statistics is equal to 1.33 and therefore, I reject the null hypothesis.
3. At 5% significant level with n-1 degree of freedom (11-1), the t-distributions critical value is 2.228 and the test t statistics is equal to 1.33 and therefore, I reject the null hypothesis.
4. At 5% significant level with n-1 degree of freedom (11-1), the t-distributions critical value is 2.228 and the test t statistics is equal to 1.33 and therefore, I accept the null hypothesis