Hypothesis Testing with Correlations and Chi-square goodness-of-fit

Part A. Hypothesis Testing with Correlations

Part A. Hypothesis Testing with Correlations (12 points)
Use Chapter 15 Data Set 1 to answer the questions below. Do the analysis using the Excel Data Analysis tool.
    a. State a null and research hypothesis related to motivation and GPA.
b. Compute the correlation between motivation and GPA. (Hint: View this video about calculating a correlation coefficient between two variables)
    b. Test for the significance of the correlation coefficient at the .05 level using a two tailed test.
    c. Write 2-3 sentences to interpret and explain your findings.

Part B. Chi-square goodness-of-fit (13 points)
The following table reports the number of men and women who successfully completed a court-ordered drug treatment program. Based on this information, do the following:
    a. Write a research hypothesis. (3 points)
b. Compute and report chi-square (4 points) (Hint: View this video, or this one, or this longer video)
    b. Write a sentence (or two) to interpret your findings. Be sure to include relevant     statistical information. (6 points)
Number of Males and Females Successfully Completing Court-Ordered Drug Treatment
Male    Female
42    28

The sampling frame included the following: only heads of households, persons 16 years of age or older who self-identified as Hispanic regardless of race, householders who worked at some pint [during the year], and householders who were employed in their own unincorporated business and professional practice…. The final sample consisted of 7,760 Hispanic self-employed persons 64% (n = 4,931) who were self-employed men and 36% (n = 2,829) who were self-employed women.

  Managerial and professional    19.0%    14.7%    χ2 = 22.27***
  Technical, sales, or administration    16.9%    20.9%    χ2 = 18.77***
  Service    8.9%    55.1%    χ2 = 2012.26***
  Farm, forestry, and fishing    14.8%    1.4%    χ2 = 359.65***
  Craft, precision production, and repair    29.4%    3.1%    χ2 = 785.47***
  Operators, fabricators, and laborers    11.0%    4.7%    χ2 = 87.99***
  
  Less than high school    48.7%    48.3%    
  High school graduate    18.9%    20.5%    χ2 = 3.07*
  Some college    22.1%    22.5%    
  Bachelor’s degree or more    10.4%    8.7%    χ2 = 5.81**
Immigrated to the United States    62.2%    62.5%    
* p < .10, ** p < .05, *** p < .01

Answer the following questions based on the article excerpt:
1. How many more men than women in the sample were self-employed?

2. For which occupation is there the largest difference between men and women?

3. What is the value of chi-square for the occupation of “Operators, fabricators, and laborers”?

4. What is the value of p for the difference between the percentage of men who are “Operators, fabricators, and laborers” and the percentage of women who are “Operators, fabricators, and laborers”?

5. Based on your answer to Question 4, should the difference be declared statistically significant?

6. Are all the differences between occupations statistically significant at the same probability level? If yes, at what level?

7. Compare the probability level for “High school graduate” with the probability level for “Bachelor’s degree or more.” Which one is more significant? Explain.

8. Should the null hypothesis be rejected for the difference in the percentages of men and women for Craft, precision production, and repair”? Why? Why not?

9. Is the difference for “Some college” statistically significant? Explain the basis of your answer.

10. Should the null hypothesis for “Immigrated to the United States” be rejected? Explain the basis for your answer.