Answer to Question #254472 in Statistics and Probability for Goldie

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-tests and t-tests are two statistical approaches for data analysis that are used in science, industry, and a variety of other fields. The Z-test and t-tests are parametric tests used to compare sample means with a reference value. A one-sample t-test is performed when we want to compare a sample mean with the population mean. The Z-test is used to test hypothesis when the population standard deviation is known and gives better results when the sample size is greater than 30. The two tests, however, are not the same. The Z-test is commonly used to determine how far a data point deviates from the data set's mean. The T-test, on the other hand, is most effective for assessing whether the sample mean differs from the true population mean statistically. T-test is applied when the population variance is unknown and the sample size is less than 30.

$b)$

The independent t-test, also known as the two sample t-test is an inferential statistical test that determines whether a statistically significant difference exist between means of two unpaired groups. The independent sample t-test is the most commonly used parametric test, however it can only compare two groups' means.

$c)$

The dependent samples t-test is used to compare the sample means of two groups that are related. This suggests that the scores for both groups are derived from the same individuals. The goal of this test is to determine if there is a significant difference in means between two groups.

$d)$

While the  independent sample t-test compares sample means for only two groups, the Analysis of variance is a statistical tool used to test equality of means among three or more independent groups. This test is usually used to compare variations among different groups relative to variations within groups.