MATH: statistic/ probablity - need help with #53(#a-c) related questions - all i

Question

MATH: statistic/ probablity
- need help with #53(#a-c) related questions
- all informations are in the pictures
- please explain answers to each questions

purchase a highly fuel-efficient vehicle. Purchase behavior was collected in one state for one year and reported below. 4-53. A unusually severe increase in gasoline prices may have motivated car buyers to low fuel prices high fuel prices 442 # of highly fuel efficient cars and trucks purchased # of ordinary cars and trucks purchased 392 36,929 42,255 Complete the row and column totals. What is the dependent variable? a. Create a relative frequency table. Is there an association between fuel prices and the number of highly fuel-efficient cars purchased? b. Unit 4: Describing Two Variable Data

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as

null, Ho: no relation b/w fure price and pruchasing cars OR fure price and pruchasing cars are independent

alternative, H1: exists a relation b/w fure price and pruchasing cars OR fure price and pruchasing cars are dependent

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =3.8415

since our test is right tailed,reject Ho when ^2 o > 3.8415

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 0.0442

critical value

the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415

we got | ^2| =0.0442 & | ^2 | =3.8415

make decision

hence value of | ^2 o | < | ^2 | and here we do not reject Ho

^2 p_value =0.8335

ANSWERS

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a. fuel price is the dependent variable

b.

we conclude that no association between the fuel price and the number of highly fuel effcient car purchased

MATRIX col1 col2 TOTALS row 1 392 442 834 row 2 36929 42255 79184 TOTALS 37321 42697 N = 80018

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