Complete Exercises 6, 8, and 9 in and submit as directed by the instructor. Use MS Word to complete “Questions to be Graded: Exercise 27” in . Submit your work in SPSS by copying the output and pasting into the Word document. In addition to the SPSS output, please include explanations of the results where appropriate. Purchase the answer to view it

Exercise 6:

To complete Exercise 6, we need to calculate the Pearson correlation coefficient between two variables. The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation.

To calculate the Pearson correlation coefficient, we can use the following formula:

r = (ΣXY – (ΣX)(ΣY)/N) / √[(ΣX^2 – (ΣX)^2 / N)(ΣY^2 – (ΣY)^2 / N)]

Where:
r = Pearson correlation coefficient
X = values of the first variable
Y = values of the second variable
Σ = summation symbol
N = number of observations

Exercise 8:

Exercise 8 requires us to analyze a research study using ANOVA. Analysis of variance (ANOVA) is a statistical test used to compare the means of three or more groups. It allows us to determine whether there are significant differences between the means of the groups.

To perform an ANOVA, we follow these steps:

1. State the null hypothesis (H0) and the alternative hypothesis (Ha). H0 assumes that there are no differences between the group means, while Ha assumes that at least one group mean is different.
2. Calculate the within-group sum of squares (SSW). This measures the variation within each group.
3. Calculate the between-group sum of squares (SSB). This measures the variation between the group means.
4. Calculate the mean squares (MSW and MSB). These are obtained by dividing the sum of squares by their respective degrees of freedom.
5. Calculate the F statistic using the formula F = MSB / MSW. The F statistic compares the variation between group means to the variation within groups.
6. Determine the critical value of F for a given significance level. Compare the calculated F statistic to the critical value to determine whether to reject or fail to reject H0.
7. Interpret the results. If the calculated F statistic is larger than the critical value, we reject H0 and conclude that there are significant differences between the group means.

Exercise 9:

In Exercise 9, we are required to calculate the chi-square statistic to test the association between two categorical variables. The chi-square test is used to determine whether there is a significant relationship between two variables in a sample population.

Here are the steps to perform a chi-square test:

1. Construct a contingency table, which shows the frequency distribution of the observed values for each category of the two variables.
2. Calculate the expected frequencies for each cell of the contingency table. These are obtained by multiplying the row total and column total for each cell and dividing by the total sample size.
3. Calculate the chi-square statistic using the formula:

χ² = ∑(O – E)² / E

Where:
χ² = chi-square statistic
O = observed frequency
E = expected frequency

4. Determine the degrees of freedom (df) for the chi-square test. It is calculated as (r – 1) x (c – 1), where r is the number of rows and c is the number of columns in the contingency table.
5. Find the critical value for the chi-square test at a given significance level and degrees of freedom.
6. Compare the calculated chi-square statistic to the critical value. If the calculated chi-square statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant association between the variables.

Please note that for Exercise 27, SPSS is used to analyze the data and provide output. It is recommended to use MS Word to copy and paste the output from SPSS and provide explanations where appropriate.

In conclusion, these exercises require different statistical techniques such as calculating the Pearson correlation coefficient, performing ANOVA, and conducting a chi-square test. Each technique has its own formula and steps to follow for analysis.