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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

Sagot :

fichoh

Answer:

0.15401

Step-by-step explanation:

Given that test statistic = 3.7408

From the question, we could deduce that, this is scenario could be analysed A ONE - WAY analysis of Variance method as it has one independent variable, Age subdivided into 3 levels

The test statistic value obtained is the Chisquare (χ²) value, which equals 3.7408

To Obtain the requested Pvalue, we need the degree of freedom, which is :

(Number of columns - 1) * (number of rows - 1)

Number of candidates = 2

Number of levels = 3

Hence,

Degree of freedom = (3 - 1) * (2 - 1) = 2 * 1 = 2

Using the Chisquare Pvalue calculator or distribution table :

χ²;3.7408, 2 = 0.154062

Pvalue = 0.1541

The probability that the observed responses is 0.15401

Given that test statistic = 3.7408

From the given , we can conclude that, this is scenario could be analysed a one -way analysis of variance method as it has one independent variable,

Age subdivided into 3 levels

The test statistic value obtained is the Chi-square (χ²) value,

Chi-square (χ²) value= 3.7408

What is the formula for degree of freedom?

(Number of columns - 1) * (number of rows - 1)

Number of candidates = 2

Number of levels = 3

Degree of freedom = (3 - 1) * (2 - 1)

= 2 * 1

= 2

Using the Chisquare Pvalue calculator or distribution table :χ²;

3.7408, 2 = 0.154062

P-value = 0.1541

Therefore,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 is 0.1541.

To learn more about the probability visit:

https://brainly.com/question/24756209

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