ANOVA Analysis.

Statistical Analysis. ANOVA Analysis. SPSS Analysis. 

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the “variation” among and between groups) used to analyze the differences among group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher.

ANOVA is a statistical method that stands for analysis of variance. ANOVA is an extension of the t and the z test and was developed by Ronald Fisher.

The specific test considered here is called analysis of variance (ANOVA) and is a test of hypothesis that is appropriate to compare means of a continuous variable.

Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not.

Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means.

NOTE: Show your work in the problems.

1. In the following situations, indicate whether you’d use the normal distribution, the tdistribution, or neither.
2. The population is normally distributed, and you know the population standard deviation.
   b. You don’t know the population standard deviation, and the sample size is 35.
   c. The sample size is 22, and the population is normally distributed.
   d. The sample size is 12, and the population is notnormally distributed.
   e. The sample size is 45, and you know the population standard deviation.
3. The prices of used books at a large college bookstore are normally distributed. If a sample of 23 used books from this store has a mean price of $27.50 with a standard deviation of $6.75, use Table 10.1 in your textbook to calculate the following for a 95% confidence level about the population mean. Be sure to show your work.
4. Degrees of freedom
   b. The critical value oft
   c. The margin of error
   d. The confidence interval for a 95% confidence level
5. Statistics students at a state college compiled the following two-way table from a sample of randomly selected students at their college:

Answer the following questions about the table. Be sure to show any calculations.

1. How many students in total were surveyed?
   b. How many of the students surveyed play chess?
   c. What question about the population of students at the state college would this table attempt to answer?
   d. State Hºand Hª for the test related to this table.
2. Answer the following questions about an ANOVA analysis involving three samples.
3. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
   b. State the null and alternate hypotheses for a three-sample ANOVA analysis.
   c. What sample statistics must be known to conduct an ANOVA analysis?
   d. In an ANOVA test, what does an Ftest statistic lower than its critical value tell us about the three populations we’re examining?

Table 10.1 Critical t Values