A market researcher for an automobile company suspects differences in preferred

Question

A market researcher for an automobile company suspects differences in preferred color between male and female buyers. Advertisements targeted to different groups should take such differences into account if they exist. The researcher examines the most recent sales information of a particular car that comes in three colors.

A. Choose the competing hypotheses to determine whether color preference depends on gender.

-H0: Color preference is independent of fender HA: color preference is dependent on gender

-H0: Color preference is dependent on gender HA: color preference is independent of gender

B. Find the critical value at the 1.0% significance level. (Round answer to decimal places)

C. Calculate the value of the test statistic. (Round the intermediate calculations to at least 4 decimal places, and final answer to two.)

D-1. What is the conclusion:

-Reject Ho: there is enough evidence to support the claim that color preference is not independent

-Reject Ho: there is not enough evidence

-Do not reject: there is enough evidence

-Do not reject: there is not enough evidence

D-2: Does your conclusion suggest that the company should target advertisements differently for vales versus females?

Color Males Female Silver 455 280 Black 525 295 Red 485 362

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: Color preference is independent of fender

alternative, H1: color preference is dependent on gender

level of significance, = 0.01

from standard normal table, chi square value at right tailed, ^2 /2 =9.21

since our test is right tailed,reject Ho when ^2 o > 9.21

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

from the table , ^2 o = 8.382

critical value

the value of |^2 | at los 0.01 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 9.21

we got | ^2| =8.382 & | ^2 | =9.21

make decision

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

^2 p_value =0.015

ANSWERS

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null, Ho: Color preference is independent of fender

alternative, H1: color preference is dependent on gender

test statistic: 8.382

critical value: 9.21

p-value:0.015

decision: do not reject Ho

no evidence that color preference depends on gender

MATRIX col1 col2 TOTALS row 1 455 280 735 row 2 525 295 820 row 3 485 362 847 TOTALS 1465 937 N = 2402

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