to investigate the relationship between age and preference for two mayoral candidates in an upcoming…

to investigate the relationship between age and preference for two mayoral candidates in an upcoming election, a random sample of city residents was surveyed. the residents were asked which candidate they preferred, and each resident was classified into one of three age - groups. the test statistic for the appropriate hypothesis test was 3.7408. approximately what is the probability that the observed responses would be as far or farther from the expected responses if there is no association between age - group and preference?\na 0.0001\nb 0.1541\nc 0.2908\nd 0.5873\ne 0.7117

to investigate the relationship between age and preference for two mayoral candidates in an upcoming election, a random sample of city residents was surveyed. the residents were asked which candidate they preferred, and each resident was classified into one of three age - groups. the test statistic for the appropriate hypothesis test was 3.7408. approximately what is the probability that the observed responses would be as far or farther from the expected responses if there is no association between age - group and preference?\na 0.0001\nb 0.1541\nc 0.2908\nd 0.5873\ne 0.7117

Answer

Explanation:

Step1: Identify the test

This is a chi - square test for independence. The degrees of freedom for a test of independence with $r$ rows and $c$ columns in a contingency table is $df=(r - 1)(c - 1)$. Here, assume 2 candidates (2 columns) and 3 age - groups (3 rows), so $df=(3 - 1)\times(2 - 1)=2$.

Step2: Use chi - square distribution

We need to find the $P(\chi^{2}_{2}\geq3.7408)$. Using a chi - square distribution table or a calculator with a chi - square distribution function (e.g., in a TI - 84 Plus: 1 - cdf("χ2cdf",0,3.7408,2)), we find the probability.

Answer:

B. 0.1541