Assignment: Testing and Inference

Instruction: Show all workings. Write up must be professional done

Summary:

Project Part 2: Assume 95% confidence level

1) Estimating using confidence interval about the mean. Use two quantitative variables
2) Hypothesis testing (Test of Significance) Use two quantitative variables same as above.
3) Test two quantitative variables for Normality
4) Test one pair of qualitative variables
5) Do Inference on Correlation(Use the same response and predictor variable as the ones you used for part 1 of the project for one pair of variables
6) Do Inference on Regression -Slope. Same variable as above

Details:

Below are guidelines to help you think through how you need to complete the other half of the project. Stay within the variables you used for part 1 so the project make sense and meaningful. (More explanation in class)

1. Estimating with confidence interval: Use slide 40 and 41 from segment 6:

i. State your sample size
ii. State your standard error
iii. State your confidence interval and interpret in plain English.
iv. Is there enough evidence to reject the null hypotheses, explain in plain English?

2. Hypotheses testing: Follow up from part 1 above: Using SPSS output:

i. State your hypotheses
ii. State your P-value
iii. Is there enough evidence to reject the null hypotheses, explain in plain English?
iv. Does your conclusion support part 1 above. Explain (Hint: Answer should be same)

3. Test two quantitative variable for Normality:

Analyze the descriptive statistics and graphs. Add your table and graph here.

Describe the shape of the distribution. (This could be copied from part I of the project)

a) What does the Boxplot and the normal probability plot shows? Explain.
b) Test for normality at 5% level of significant (α = 0.05)

i. Calculate the Z value for Skewness. Is it within 95% confidence level? Explain
ii. Calculate Z value for Kurtosis. Is it within 95% confidence level? Explain
iii. State your hypotheses
iv. From Shapiro Wilk test state the P-value
v. Compare the P-value to α. Is P-value greater than of less than α
vi. Is there enough evidence to reject normality? Explain your conclusion in plain English
vii. Is the normality test different by qualitative variable you chose? Explain

4. Testing Qualitative variables: Two way contingency table:

Use the same qualitative variables you worked with in part 1 of the project.

Using SPSS, create a crosstab with table with Expected count. Create a Chi-Square table and clustered bar chart of your variables. Copy and paste relevant tables and graphs to your word document. Now do testing and interpret in plain English?

What is your degree of freedom (df)?

a) State the hypotheses and test for association/Independence between your variables.

i. Write your conclusion in plain English

b) State the hypotheses and test for Goodness of fit

i. Write your conclusion in plain English

5. Correlation: Follow up from part 1 of the project. Re-Copy relevant table here. (a) &(b) is already done in part 1 of the project, you only need to recall it here an proceed to (c)-(e)

(a) What is the response variable and the independent variable in this study?

(b) Compute the correlation coefficient and draw conclusions (in simple language), on the strength of the association between the two variables.

(c) State the hypotheses and do inference on correlation

(d) What is the p-value

(e) Based on (c), can we conclude that correlation is significant? Explain

6. Regression: Follow up from part 1 of the project. Copy all relevant table here. (a)-(c) is already done in part 1 of the project, you only need to recall it here an proceed to (d)

(a) Find the regression line of Y on X. Write down the regression line to predict Y from X. Make sure to use the names of the variables not X and Y

(b) What is the slope of the fitted regression line? Explain in simple language what the slope value indicates about the relationship between response and predicted variable.

(c) What is the coefficient of determination, R2 for the regression line? Explain in simple language what the R2 value says about the regression line to predict Y.

(d) Check that the response variable and the predictor variable met the conditions for regression inference, namely, the relationship is linear, the response variable is approximately normally distributed, the observation is independent and the standard deviation of the response variable is the same for all values of the predictor variable. State any limitations here. As long as some of the assumption are met proceed to inference below

i. State degree of Freedom, df?
ii. What is the confidence interval for regression slope? Interpret in plain English.
iii. Test the Hypothesis of no relationship versus relationship exist.
iv. State that hypotheses
v. What is t from SPSS output? Explain what the value means
vi. What is the p-value for the stated hypotheses in part iiiabove?
vii. At 5% level of significance, what is your conclusion (explain in plain English)?

Submission

All relevant graphs and tables must be copied over first and then interpretations below them. Please follow the format of the Project sample.
Any limitations of your project must be stated. How would you project be different if you have access to more info or more data should be included too.