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Exercises for Question Type 5: Calculating the chi-squared value and/or p-value to conclude the chi-squared independence test - IB | RevisionDojo

Question 1

Skill question

A study on two factors produces the following 2×2 table of observed counts:

\begin{array}{c|cc} & \text{Disease Present} & \text{Disease Absent} \\ \hline \text{Smoker} & 40 & 60 \\ \text{Non-Smoker} & 30 & 70 \end{array}

Calculate the chi-squared statistic for testing independence between smoking and disease status.

Question 2

Skill question

The following 2×2 table shows observed frequencies of a treatment vs recovery outcome:

\begin{array}{c|cc} & \text{Recovered} & \text{Not Recovered} \\ \hline \text{Treatment A} & 50 & 30 \\ \text{Treatment B} & 20 & 40 \end{array}

Perform a chi-squared test for independence at the 5% significance level. Calculate the test statistic and state your conclusion.

Question 3

Skill question

You conduct a chi-squared test and obtain $\chi^2 = 4.605$ with 1 degree of freedom. Find the p-value and conclude at the 5% level.

Question 4

Skill question

A survey records eye colour (Blue, Green, Brown) and blood type (A, B, O). The observed counts are:

Blue: A=15, B=10, O=25 Green: A=20, B=5, O=15 Brown: A=30, B=20, O=10

Calculate the chi-squared statistic for testing independence.

Question 5

Skill question

A 2×4 table yields the following observed counts:

Group1: 10, 20, 30, 40 Group2: 30, 25, 20, 15

Compute $\chi^2$ and test independence at 5%.

Question 6

Skill question

The following table records preference for a new product (Like, Neutral, Dislike) by gender:

Male: Like=40, Neutral=30, Dislike=10 Female: Like=35, Neutral=25, Dislike=30

Test at the 5% level whether preference is independent of gender.

Question 7

Skill question

Observed counts for two age groups (Under 30, 30 & Over) and four media usage categories (Daily, Weekly, Monthly, Never) are:

Under 30: Daily=60, Weekly=30, Monthly=10, Never=0 30 & Over: Daily=40, Weekly=50, Monthly=30, Never=10

Test independence at 1% by computing $\chi^2$ and p-value.

Question 8

Skill question

A 3×3 contingency table yields $\chi^2 = 12.5$ for an independence test. Calculate the p-value.

Question 9

Skill question

Five performance levels (Poor, Fair, Good, Very Good, Excellent) are crossed with gender, yielding a 5×2 table with $\chi^2=13.8$ . How many degrees of freedom and what is the p-value? Draw a conclusion at 5%.

Question 10

Skill question

In four regions (North, South, East, West), counts of product adoption (Yes/No) are recorded:

           Yes  No

North 25 15 South 30 20 East 20 10 West 15 25

Compute the chi-squared statistic and its p-value, then state if adoption is independent of region at 5%.

Question 11

Skill question

A 3×4 table of survey counts has grand total 200 and $\chi^2 = 18.7$ . How many degrees of freedom does the test have, and what is the p-value?

Question Type 5: Calculating the chi-squared value and/or p-value to conclude the chi-squared independence test Exercises