Answer to Question #266323 in Statistics and Probability for Elma

Question

Getting acquainted with the essential terms and concepts on Analysis of Variance

(ANOVA), it is now time for you to explain thoroughly your answers to the questions found

below.

1. Explain the usage of the following statistical tools in testing the hypotheses.

a. Testing One Sample Mean using t-test and z-test.

b. Testing Two Independent Sample Mean

c. Testing Dependent Sample Mean.

d. Analysis of Variance

Answer 1

a) Z-test and t-test are statistical tools in data analysis that have many applications in various disciplines such as business, science etc. Both tests are used to compare the means of a sample to a specific reference. However, the two tests differ. Z- test is mostly used to tell how far a data point is from the mean of a data set. It can also be used to test hypothesis when the standard deviation is known and the sample size is large, this is >30. T-test on the hand is mostly useful in determining if there is statistically significant difference between the sample mean from the true population mean. It is used when the standard deviation is unknown and the sample size is quite small.

b) Testing two independent sample mean simply compares two independent groups by determining the difference in their means and testing whether that difference is statistically significant. The independent sample t-test is the mostly preferred parametric test, but it is limited to only means for two groups.

c) The dependent sample t-test or the paired t-test is used to compare means which are related. It is also used to determine whether the difference in the means of two dependent sets of observation is statistically different from 0.

d) Unlike the independent sample t-test, the Analysis of variance is used to test equality among several means. it is mostly used to compare variations among different groups relative to variations within groups.