Question

A sample of n = 16 individuals is selected from a population with µ = 40 and σ = 12, and a treatment is administered to the sample. After treatment, the sample mean is M = 42. You are asked to determine if the sample is still the same as the population. Using an alpha of .05 and a directional (one-tailed) hypothesis because you expect an increase in your sample mean due to the treatment, conduct a one-sample z-test and determine whether the sample is significantly different from the population. [G&W Chp 8] z = 0.667, and you determine that the sample IS significantly different from the population. z = 0.667, and you determine that the sample IS NOT significantly different from the population. z = 1.965, and you determine that the sample IS significantly different from the population. z = 1.965, and you determine that the sample IS NOT significantly different from the population. z = 2.638, and you determine that the sample IS significantly different from the population. z = 2.638, and you determine that the sample IS NOT significantly different from the population.

Answer 1

Here the answer is z = 0.667, and you determine that the sample IS NOT significantly different from the population.

Now, the test statistic is z = = = 0.667

Now, it is a right-tailed test because our hypothesis is _{vs .}

So, the P-value of the test is P[Z > 0.667] = 0.2523861 [Here Z follows normal distribution with mean 0 and variance 1]

P-value is greater than 0.01 so we can't reject the null hypothesis. So, our conclusion is we don't have sufficient evidence to say that the sample is different from the population.