Complete the questions below to the best of your ability. TYPE your response (Ha

Question

Complete the questions below to the best of your ability. TYPE your response (Handwritten response will NOT be accepted) and use additional space (as required)

A researcher is studying the determinants of state-financed welfare programs in the United States. She hypothesizes that the average income in a state is associated with the number of welfare programs the state legislature will adopt. She obtains data pertaining to the average income of the residents of each state (coded “low” and “high”) and the number of welfare programs passed by each state legislature (coded “few” and “many”). These data yielded the Table below:

(7 Points) Complete the contingency or crosstabulation Table below (include percentages, marginal totals and grand total)

Average Income

                                                            Low                             High             Total   ____________

Number of Welfare Programs

Few                                         9 ( _ %)                       16 ( _ %)            ___ ( __%)                 

Many                                       11 ( _ %)                      14 ( _ %)            ___ ( __%)                 

Total                                        ___      __ ( __%)                    __( __%)            ___ ( __%)      ______

b.     (4 Points) State a two-tailed null and alternative hypotheses for this information

Null hypothesis (Ho): ____________________________________________________________

____________________________________________________________________________________________________________________________________________________________

Alternative hypothesis (HA): ______________________________________________________

____________________________________________________________________________________________________________________________________________________________

(2 Points) Identify the dependent and independent variables from the Table

Dependent Variable _____________________________________________________________

Independent Variable ____________________________________________________________

(4 Points) Describe (interpret) the Table: _________________________________________

__________________________________________________________________________________________________________________________________________________________________________________

(6 Points) Using the data from the table (comparing percentage across “low” and “high” income), will you say that there is evidence in support of the hypothesis? Justify your response __________________________________________________________________

_______________________

2.     Do men and women differ in their preference for Coca cola and Pepsi cola?

To answer this question, we selected a sample of 100 people (35 men and 65 women) and perform a taste preference test. After the taste preference test, we found 40 people (30 male and 10 female) prefer Coca-cola and the remaining 60 (5 male and 55 female) prefer Pepsi Cola.

(9 Points) Present the information in appropriate contingency or crosstabulation Table (Use the template below; providing the numbers, percentages, marginal totals and grand total)

Gender

                                                Male                            Female                        Total   ____________

Drink Type

Coca Cola                  

Pepsi Cola                  

Total                                       _______________                                                                             

b.     (4 Points) State a two-tailed null and alternative hypotheses for this information

Null hypothesis (Ho): ____________________________________________________________

____________________________________________________________________________________________________________________________________________________________

Alternative hypothesis (HA): ______________________________________________________

____________________________________________________________________________________________________________________________________________________________

(2 Points) Identify the dependent and independent variables from the Table

Dependent Variable _____________________________________________________________

Independent Variable ____________________________________________________________

(4 Points) Describe (interpret) the Table: _

(6 Points) Using the data from the table (comparing percentage across “male” and “female”), will you say men and women differ in their preference for Coca-cola and Pepsi cola? Justify your response. If there is the gender difference in preference, what is the nature of the difference in preference (i.e. which sex prefers more/less of which type of drink)?

(4 Points) Explain why in statistical testing the null hypothesis is rejected when the test value exceeds or is equal to the critical value. ___

Explanation / Answer

here we go for chi-squre test for independency of attributes

Ho: there is no relationship between average income and welfare program

Ha: there is dependency between average income and welfare program

  Average Income

Number of Welfare Programs Low High total

Few 9 16 25

Many 11 14 25

20 30 50

E(9)=25x20/50, E(16)=25x30/50,E(11)=20x25/50, E(14)=30x25/50

chi-square statistic=(O-E)2/E with df=1

here O are 9,16,11,14 and

E are 10,15,10,15

chi-squre=0.3333

P=0.5637

since P is more than 0.05 so we say that at 5% level of significance we reject alternative hypothesis and accept null hypothesis that  there is no relationship between average income and welfare program.

conclusion:High average income in a state does not tend to lead to the passage of welfare programs."

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