Discussion B:  Discussion B:  Frequency Tables Week 3 Post (300+ words): Think of some discrete random variable you observe on a regular basis. For example, it could be the (rounded) number of hours you sleep, how many gallons of gas are in your car when you get into it, how many boxes of cereal are in your house, how many days between grocery shopping, etc. (just make sure it takes only integer values). Try to list all of the possible values that this discrete random variable can take. If you can, collect some frequency data – give the relative frequency table and use this as an estimate of the probability distribution. Calculate the expected value and the standard deviation for this probability distribution. Interpret these parameters, and discuss whether they make sense based on your experience. Week 4 Responses (100+ words, x2): Look at your classmates’ distribution. Is there any well-known distribution that could be used to model their random phenomenon? Some well-known discrete distributions are: Uniform, Bernoulli, Binomial, Geometric, and Poisson (but there are others). Explain why this distribution might be appropriate. Post a picture of the discrete distribution and a histogram of the frequency data from the original post, and comment on what is similar and different. Are there any outliers that, if removed, would make the frequency data match the distribution really well? Week 3 Post (300+ words): Think of some discrete random variable you observe on a regular basis. For example, it could be the (rounded) number of hours you sleep, how many gallons of gas are in your car when you get into it, how many boxes of cereal are in your house, how many days between grocery shopping, etc. (just make sure it takes only integer values). Try to list all of the possible values that this discrete random variable can take. If you can, collect some frequency data – give the relative frequency table and use this as an estimate of the probability distribution. Calculate the expected value and the standard deviation for this probability distribution. Interpret these parameters, and discuss whether they make sense based on your experience. Responses (100+ words, x2): Look at your classmates’ distribution. Is there any well-known distribution that could be used to model their random phenomenon? Some well-known discrete distributions are: Uniform, Bernoulli, Binomial, Geometric, and Poisson (but there are others). Explain why this distribution might be appropriate. Post a picture of the discrete distribution and a histogram of the frequency data from the original post, and comment on what is similar and different. Are there any outliers that, if removed, would make the frequency data match the distribution really well?

1. Say you've obtained a chi-square of 12.56. You have a chi square critical value of 3.481. Based on this information, what do you conclude?A) Fail to reject the null hypothesis B) Reject the Null Hypothesis 2. Say you’ve obtained a chi-square of 10.95. You have a chi square critical value of 9.210. Based on this information, what do you conclude?A) Fail to reject the null hypothesis B) Reject the Null Hypothesis 3. For the table below, what would be the chi-square critical value if you were doing a hypothesis test and your significance level was 0.01? Counseling for Mental Problems Total Yes No Do you have Kids? Yes 39 695 734 No 19 256 275 Total 58 951 1009 A 3.841 B 6.635 C 5.991 D 9.210 4) For the table below, what is the expected frequency for Yes Demoted and Pretty Happy? (Remember that you don't need to do all the expected frequencies to get just one…) General Happiness Total Very Happy Pretty Happy Not Too Happy Were Demoted? Yes 5 12 7 24 No 294 545 99 938 Total 299 557 106 962 7 14 3 543 5. For the table below, what is the expected frequency for No Kids and Yes Counseling for Mental Problems? (Remember that you don’t need to do all the expected frequencies to get just one…) Counseling for Mental Problems Total Yes No Do you have Kids? Yes 39 695 734 No 19 256 275 Total 58 951 1009 42 16 692 259 6. For the table below, what is the expected frequency for No Demoted and Not too Happy? (Remember that you don't need to do all the expected frequencies to get just one…) General Happiness Total Very Happy Pretty Happy Not Too Happy Were Demoted? Yes 5 12 7 24 No 294 545 99 938 Total 299 557 106 962 7 292 103 543 7. For the table below, what is the expected frequency for No Kids and No Counseling for Mental Problems? (Remember that you don’t need to do all the expected frequencies to get just one…) Counseling for Mental Problems Total Yes No Do you have Kids? Yes 39 695 734 No 19 256 275 Total 58 951 1009 42 16 692 259 8. In the table below, what is the column marginal for “ever had home broken into = no”? Ever had home broken into? Gender Yes No Total Female 1558 1064 2622 Male 1567 1069 2636 Total 3125 2133 5258 3125 2133 2622 2636 9. For the table below, what is the chi-square? (Remember, you can round to whole numbers for the expected frequency, but leave at least 2 decimal places on for all other chi-square calculations). Counseling for Mental Problems Total Yes No Do you have Kids? Yes 39 695 734 No 19 256 275 Total 58 951 1009 0.04 0.94 0.36 0.82 10. For the table below, what is the chi-square? (Round this way or the answer will not turn out right: you can round to whole numbers for the expected frequency, but leave at least 2 decimal places on for all other chi-square calculations). Choose the answer that is closest. General Happiness Total Very Happy Pretty Happy Not Too Happy Were Demoted? Yes 5 12 7 24 No 294 545 99 938 Total 299 557 106 962 6.92 2.69 5.96 4.85 11. You've obtained a chi square of 34.56, and it's significant. You want to test how strong the relationship between these two variables is. You have a sample size of 75. You have a table with 2 rows and 4 columns. What's your Cramer's V? 0.46 0.68 0.26 0.53 12. Say you have a phi-coefficient of 0.51. How strong is the relationship between the two variables it tests? Weak Relationship Moderate Relationship Strong Relationship 13. You’ve obtained a chi square of 10.98, and it’s significant. You want to test how strong the relationship between these two variables is. You have a sample size of 50. What’s your phi-coefficient? 0.47 0.56 0.22 0.25 14. You’ve obtained a chi square of 16.52, and it’s significant. You want to test how strong the relationship between these two variables is. You have a sample size of 75. What’s your phi-coefficient? 0.47 0.22 0.69 0.18 15. Is the interpretation of the following regression line correct?Regression line: y ⏜ = 20.5 + 1.4 ( x ) Interpretation: For every one unit increase in y, there is a 1.4 increase in x. True False 16. Is the interpretation of the following regression line correct?Regression line: y ⏜ = 0.89 + 2.3 ( x ) Interpretation: For every one unit increase in y, there is a 0.89 increase in x. True False 17. Is the interpretation of the following regression line correct?Regression line: y ⏜ = 0.5 − 1.7 ( x ) " style="max-width: 694px;" rel="max-width: 694px;"> y ⏜ = 0.5 − 1.7 ( x ) Interpretation: For every one unit increase in x, there is a 1.7 decrease in y. True False 18. What type of relationship, positive or negative, is portrayed in the following sentence? When crime worsens, individuals' willingness to help their neighborhoods decreases. Positive Negative 19. What type of relationship, positive or negative, is portrayed in the following sentence? The statistical relationship shows that when foreclosure rates increase, crime worsens. Positive Negative 20. Find the correlation between the two following variables: % of people in neighborhood on welfare and the number of people who have police contact. x y 40 9 59 25 20 3 15 10 0.832 0.895 0.790 0.867 21. What is the strength of the following correlation? 0.156 Weak Moderate Strong 22. What is the strength of the following correlation? 0.451 Weak Moderate Strong 23. A friend of yours suggests that at least 10% of people at your university have had something stolen from them on campus in the past year. This is your population value. You take a random sample of 100 people in you classes to determine if your friend is correct, you think that they may be wrong. You find that 15% of them have had something stolen. Would you use z or t to test this hypothesis? Z Distribution T Distribution 24. A friend of yours suggests that at least 10% of people at your university have had something stolen from them on campus in the past year. This is your population value. You take a random sample of 100 people in you classes to determine if your friend is correct, you think that they may be wrong. You find that 15% of them have had something stolen. Would you have a one or two tailed test? One tailed Two Tailed 25. A friend of yours suggests that at least 10% of people at your university have had something stolen from them on campus in the past year. This is your population value. You take a random sample of 100 people in you classes to determine if your friend is correct. You find that 15% of them have had something stolen. What is the value of your test statistic? 1.667 2.112 1.521 1.231 26. What are the age differences among teens that report being delinquent (or not)? Conduct a two mean hypothesis test to ascertain whether there is an age difference between teens who report being delinquent and teens that report no delinquency. Use a significance level of α = 0.05 and the information below. No Delinquency Delinquent n = 21 n = 5 s1 = 0.6 s2 = 1.6 x1 = 13 x2 = 17 Would the alternative hypothesis for this test be directional or non-directional? Directional, greater than Directional, less than Non-Directional 27. Let’s say we believe that desk-officers and patrol-officers spend different get differing numbers of overtime hours because of their different assignments. We take a small sample of each group to determine if they are truly different. Conduct a two mean hypothesis test to ascertain whether there is a difference between desk-officers and patrol-officers regarding overtime. Use a significance level of α = 0.01 and the information below. Desk Officers Patrol Officers n = 4 n = 7 s1 = 2.9 s2 = 2.0 x ¯ 1 = 3 x ¯ 2 = 5 What do you conclude? Reject H0 Fail to Reject H0 28. Let’s say we believe that desk-officers and patrol-officers spend different get differing numbers of overtime hours because of their different assignments. We take a small sample of each group to determine if they are truly different. Conduct a two mean hypothesis test to ascertain whether there is a difference between desk-officers and patrol-officers regarding overtime. Use a significance level of α = 0.01 and the information below. Desk Officers Patrol Officers n = 4 n = 7 s1 = 2.9 s2 = 2.0 What is your critical value(s) for this test? ± 2.056 ± 2.365 ± 3.250 ± 2.831 29. Let’s say we believe that desk-officers and patrol-officers spend different get differing numbers of overtime hours because of their different assignments. We take a small sample of each group to determine if they are truly different. Conduct a two mean hypothesis test to ascertain whether there is a difference between desk-officers and patrol-officers regarding overtime. Use a significance level of α = 0.01 and the information below. Desk Officers Patrol Officers n = 4 n = 7 s1 = 2.9 s2 = 2.0 What is the degrees of freedom for this test? 9 11 8 6 30. What are the age differences among teens that report being delinquent (or not)? Conduct a two mean hypothesis test to ascertain whether there is an age difference between teens who report being delinquent and teens that report no delinquency. Use a significance level of α = 0.05 and the information below. No Delinquency Delinquent n = 21 n = 5 s1 = 0.6 s2 = 1.6 What is your obtained t? - 10.211 8.722 -9.430 -16.11