Question

Background: Morris Saldov conducted a study in Eastern and Central Newfoundland in 1988 to examine public attitudes towards social spending. In particular, the study tried to determine if knowing someone on public assistance (yes, no) affected one's views on social spending (too little, about right, too much). The data from the study is summarized in the table below.

	Yes	No	Total
Too little	38	7	45
About right	17	13	30
Too much	8	7	15
Total	63	27	90

Source: Morris Saldov, Public Attitudes to Social Spending in Newfoundland," Canadian Review of Social Policy, 26, November 1990, pages 10-14.

1. Compute the test statistic.
   
   Complete the following table of expected counts. (Round your answers to 2 decimal places).
   

   	Yes	No
   Too little
   About right
   Too much

   
   Compute the value of the test statistic. (Round your answer to 2 decimal places.)
   
   χ2=χ2=
   
2. Compute the p-value. (Round your answer to 4 decimal places.)
   
   pp-value =  

You are interested in investigating whether the type of computer a person primarily uses and the type of car they drive are dependent. The table below shows the results of a survey.

Frequencies of Computer and Car Types

	Sedan	SUV	Truck
Tablet	75	91	53
Notebook	93	98	38
Desktop	129	119	29

What can be concluded at the αα = 0.10 significance level?

1. The test-statistic for this data = Incorrect (Please show your answer to three decimal places.)
   
2. The p-value for this sample = Incorrect(Please show your answer to four decimal places.)  

In Milwaukee, they randomly sampled 280 female voters, and 220 male voters. They collected data on the respondent's opinion on building a new sports stadium. We want to know whether there is good evidence that one's gender influences whether a person is for or against the new stadium. Use αα = 0.05.

	For Bond Issue	Against Bond Issue	Total
Men	77	203	280
Women	14	206	220
Total	91	409	500

c) Chi Square Test Statistic = Incorrect 1 decimal place

Answer 1

a.

Given table data is as below MATRIX col1 col2 TOTALS row 1 38 7 45 row 2 17 13 30 row 3 8 7 15 TOTALS 63 27 N = 90 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N row 3 row3*col1/N row3*col2/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 31.5 13.5 row 2 21 9 row 3 10.5 4.5 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 38 31.5 6.5 42.25 1.341 7 13.5 -6.5 42.25 3.13 17 21 -4 16 0.762 13 9 4 16 1.778 8 10.5 -2.5 6.25 0.595 7 4.5 2.5 6.25 1.389 ᴪ^2 o = 8.995 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, α = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =5.991 since our test is right tailed,reject Ho when ᴪ^2 o > 5.991 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 8.995 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 5.991 we got | ᴪ^2| =8.995 & | ᴪ^2 α | =5.991 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0.011 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 8.995 critical value: 5.991 p-value:0.011 decision: reject Ho

we have enough evidence to support the claim that  if knowing someone on public assistance (yes, no) affected one's views on social spending (too little, about right, too much).

b.

Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 75 91 53 219 row 2 93 98 38 229 row 3 129 119 29 277 TOTALS 297 308 120 N = 725 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 col3 row 1 row1*col1/N row1*col2/N row1*col3/N row 2 row2*col1/N row2*col2/N row2*col3/N row 3 row3*col1/N row3*col2/N row3*col3/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 row 1 89.714 93.037 36.248 row 2 93.811 97.286 37.903 row 3 113.474 117.677 45.848 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 75 89.714 -14.714 216.502 2.413 91 93.037 -2.037 4.149 0.045 53 36.248 16.752 280.63 7.742 93 93.811 -0.811 0.658 0.007 98 97.286 0.714 0.51 0.005 38 37.903 0.097 0.009 0 129 113.474 15.526 241.057 2.124 119 117.677 1.323 1.75 0.015 29 45.848 -16.848 283.855 6.191 ᴪ^2 o = 18.542 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, α = 0.1 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =7.779 since our test is right tailed,reject Ho when ᴪ^2 o > 7.779 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 18.542 critical value the value of |ᴪ^2 α| at los 0.1 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 3 - 1 ) = 2 * 2 = 4 is 7.779 we got | ᴪ^2| =18.542 & | ᴪ^2 α | =7.779 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0.001 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 18.542 critical value: 7.779 p-value:0.001 decision: reject Ho

we have enough evidence to support the claim that  whether the type of computer a person primarily uses and the type of car they drive are dependent.

c.

Given table data is as below MATRIX col1 col2 TOTALS row 1 77 203 280 row 2 14 206 220 TOTALS 91 409 N = 500 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 50.96 229.04 row 2 40.04 179.96 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 77 50.96 26.04 678.08 13.3062 203 229.04 -26.04 678.08 2.9605 14 40.04 -26.04 678.08 16.9351 206 179.96 26.04 678.08 3.768 ᴪ^2 o = 36.9698 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, α = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =3.8415 since our test is right tailed,reject Ho when ᴪ^2 o > 3.8415 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 36.9698 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415 we got | ᴪ^2| =36.9698 & | ᴪ^2 α | =3.8415 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 36.9698 critical value: 3.8415 p-value:0 decision: reject Ho

we have enough evidence to support the claim that  whether there is good evidence that one's gender influences whether a person is for or against the new stadium.