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Grade 9 Chi-Square Test Worksheet

This worksheet provides exercises on the Chi-Square test, covering concepts like null hypotheses, degrees of freedom, and calculating the chi-square statistic for categorical data.

Grade 9 Math Probability and StatisticsChi-square Test
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Fill in the BlanksMultiple ChoiceShort AnswerTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.HSS.IC.B.5
7 sections · Free to use · Printable
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Grade 9 Chi-Square Test Worksheet

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Read each question carefully and provide your answers in the spaces provided. Show all your work for calculations.

1. The Chi-square test is used to determine if there is a significant   between two categorical variables.

2. The null hypothesis (H₀) in a Chi-square test typically states that there is   association between the variables.

3. The degrees of freedom for a contingency table are calculated as (rows - 1) × (  - 1).

1. Which of the following is NOT an assumption of the Chi-square test?

a

Random sampling

b

Normally distributed data

c

Independent observations

d

Expected frequencies > 5

2. What happens to the critical Chi-square value as the degrees of freedom increase (for a constant significance level)?

a

It decreases

b

It increases

c

It stays the same

d

It depends on the data

1. A researcher wants to investigate if there is a relationship between gender and preference for a certain type of music (Pop, Rock, Classical). What would be the null hypothesis for this study?

2. Explain the concept of 'expected frequency' in the context of a Chi-square test.

1. A high Chi-square test statistic value suggests that there is a strong association between the observed and expected frequencies.

T

True

F

False

2. If the p-value from a Chi-square test is less than the significance level (e.g., 0.05), we fail to reject the null hypothesis.

T

True

F

False

A survey was conducted to see if there is a relationship between gender and preference for coffee or tea. The observed frequencies are given in the table below:

Coffee Tea Total

Males 40 20 60

Females 30 50 80

Total 70 70 140

1. Calculate the expected frequency for 'Males' who prefer 'Coffee'.

2. Calculate the Chi-square statistic (χ²) for this data. (Show your steps and formula).

3. Determine the degrees of freedom for this test.