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# Chi-Square Test of Goodness of fit & Association

For the three problems:

A) State the hypotheses and identify the claim
B) Find the critical value(s)
C) Compute the test value
D) Make the decision
E) Summarize the results

1: A researcher reads that the marital status of U.S. adults is distributed as follows: marries, 60%; single, 24%; divorced,10%; widowed 6%. She selects a sample of 150 people, and the results are shown. At alpha = 0.05, test the claim that shoppers have no preference. Give one example of how retail merchants would be able to use the numbers in this study.

Marital Status Married Single Divorced Widowed
Number 72 42 21 15

2: A car manufacturer wishes to determine whether the type of car purchased is related to the individual's gender. The data obtained from a sample are shown here. At alpha = 0.011, is the gender of the purchaser related to the type of car purchased?

Gender of purchaser Sedan Compact Station Wagon SUV
Male 33 27 23 17
Female 21 34 41 18

3: A researcher surveyed 50 randomly selected males and 50 randomly selected females to see how they paid their bills. The data are shown. At alpha = 0.01, test the claim that the proportions are not equal. What might be a reason for the difference, if one exists?

Type of payment Checks Electronically In person
Males 27 15 8
Females 22 19 9
Total 49 34 17

#### Solution Preview

For the three problems I need to find the:

A) State the hypotheses and identify the claim
B) Find the critical value(s)
C) Compute the test value
D) Make the decision
E) Summarize the results

1: A researcher reads that the martial status of U.S. adults is distributed as follows: marries, 60%; single, 24%; divorced,10%; widowed 6%. She selects a sample of 150 people, and the results are shown. At œ=0.05, test the claim that shoppers have no preference. Give one example of how retail merchants would be able to use the numbers in this study.

Marital Status Married Single Divorced Widowed
Number 72 42 21 15

A) State the hypotheses and identify the claim

The null hypothesis tested is

H0: Shoppers have no preference.

The alternative hypothesis is

H1: Shoppers have preference.

Claim: Null hypothesis

B) Find the critical value(s)

Critical value is obtained from the Chi-square distribution table with d.f. 3 at the significance level 0.05.

Critical value = 7.8147

C) Compute the test value

The test Statistic used is where O is the observed frequency and E is the expected frequency.

The Expected frequencies are given below.

Observed Expected O - E (O - E)² / E % of ...

#### Solution Summary

The solution provides step by step method for the calculation of chi square test for goodness of fit and association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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