Hypothesis Testing

A sample of size of n=13 has a mean of x̄=11 and a standard deviatoin of s=6.15088059238412. Given a population mean of μ=11.06151 and a population standard deviation of σ=1.705947, does the sample provide sufficient evidence that the actual population mean is less than 11.06151 at a 99% level of confidence?

New Example

1. State the null hypothesis H₀ and alternative hypothesis H_a.
2. Determine the significance level (α) and appropriate distribution to use.
3. Calculate the test statistic.
4. Determine whether to reject or fail to reject the null hypothesis H₀.
5. State the conclusion.

Solution