Question Type 3: Initiating the chi-squared independence test with the hypothesis and critical regions Exercises

A factory records defect occurrence by shift (Day, Night) and defect type (Minor, Major, Critical). Counts: Day — 12, 7, 3; Night — 9, 11, 2. For a chi-squared independence test, specify $H_0$, $H_1$, the degrees of freedom, and the critical region at the 5% level.

An email campaign’s response is recorded by customer segment (New, Returning, VIP) and action (Open, Click). Observed counts are given. For the chi-squared test of independence, state $H_0$, $H_1$, compute degrees of freedom, and specify the critical region at the 10% significance level.

A survey records preferences between Marvel and DC by gender: Male — 30 Marvel, 40 DC; Female — 14 Marvel, 15 DC. For a chi-squared test of independence, state suitable hypotheses, the degrees of freedom, and the critical region at the 5% significance level.

A health study records smoking status (Smoker, Non-smoker) and presence of a condition (Present, Absent). Counts: Smoker — 42 present, 58 absent; Non-smoker — 30 present, 90 absent. For a chi-squared independence test, provide $H_0$, $H_1$, the degrees of freedom, and the critical region at the 1% significance level.

Website visitors are grouped by device (Mobile, Desktop) and browser (Chrome, Safari, Firefox, Other). Counts: Mobile — 180, 60, 30, 30; Desktop — 90, 45, 35, 20. State $H_0$, $H_1$, the degrees of freedom, and the critical region at the 10% significance level for a chi-squared test of independence.

Purchases are categorized by region (North, East, South, West) and payment method (Card, Cash). Counts: North — 45, 20; East — 30, 15; South — 28, 22; West — 25, 18. For a chi-squared test of independence, give $H_0$, $H_1$, the degrees of freedom, and the critical region at the 5% level.

Commuters are classified by travel mode (Car, Bus, Train) and time of travel (Peak, Off-peak). Observed counts: Peak — Car 62, Bus 25, Train 33; Off-peak — Car 38, Bus 30, Train 22. For a chi-squared test of independence, state $H_0$, $H_1$, the degrees of freedom, and the critical region at the 10% significance level.

A survey classifies customers by age band (18–29, 30–44) and preferred news source (TV, Online, Print, Radio, Other). Observed counts are recorded. For a chi-squared test of independence, give $H_0$, $H_1$, the degrees of freedom, and the critical region at the 1% significance level.

Students are grouped by education level (High school, Undergraduate, Postgraduate) and preferred streaming platform (A, B, C). Observed counts: HS — 24, 18, 8; UG — 31, 27, 12; PG — 15, 16, 11. Initiate a chi-squared independence test: state $H_0$, $H_1$, degrees of freedom, and the critical region at the 1% significance level.

Students are categorized by study habit (Morning, Afternoon, Night) and result (Pass, Fail, Withdraw, Distinction). For initiating a chi-squared independence test, state $H_0$, $H_1$, determine the degrees of freedom, and give the critical region at the 5% level.

Employees are classified by department (Sales, HR, Engineering, Support, Finance) and training completion status (Completed, Not completed, In progress). Sample counts are recorded in a $5\times 3$ table. For a chi-squared test of independence, state $H_0$, $H_1$, compute the degrees of freedom, and specify the critical region at the 5% significance level.

TV viewers are categorized by time slot (Morning, Afternoon, Evening, Late Night) and preferred genre (News, Drama, Sports). For initiating a chi-squared independence test, provide $H_0$, $H_1$, the degrees of freedom, and the critical region at the 1% significance level.