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

Website visitors are grouped by device (Mobile, Desktop) and browser (Chrome, Safari, Firefox, Other). The observed counts are as follows:

• 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.

Students are grouped by their education level (High school, Undergraduate, Postgraduate) and their preferred streaming platform (A, B, C). The observed counts are shown below:

Initiate a chi-squared independence test: state $H_0$, $H_1$, the degrees of freedom, and the critical region at the 1% 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 the null hypothesis $H_0$, the alternative hypothesis $H_1$, the degrees of freedom, and the critical region at the 1% significance level.

TV viewers are categorized by time slot (Morning, Afternoon, Evening, Late Night) and preferred genre (News, Drama, Sports). For initiating a $\chi^2$ independence test, provide $H_0$, $H_1$, the degrees of freedom, and the critical region at the 1% significance level.

A factory records the number of defects occurring during different shifts (Day and Night) and of different types (Minor, Major, and Critical). The observed frequencies are summarized in the following contingency table:

For a chi-squared test of independence at the $5\%$ significance level:

(a) State the null and alternative hypotheses. (b) Determine the number of degrees of freedom. (c) State the critical value and the corresponding rejection region.

A health study records smoking status (Smoker, Non-smoker) and the presence of a medical condition (Present, Absent). The observed counts are:

• Smoker: 42 present, 58 absent
• Non-smoker: 30 present, 90 absent

For a chi-squared test for independence at the 1% significance level, state the null and alternative hypotheses, calculate the degrees of freedom, and determine the critical region.

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

Purchases are categorized by region (North, East, South, West) and payment method (Card, Cash). The counts are as follows: North — 45, 20; East — 30, 15; South — 28, 22; West — 25, 18.

For a chi-squared test of independence, state the null and alternative hypotheses, find the degrees of freedom, and determine 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 are shown in the following table:

For a $\chi^2$ test of independence, state: (a) $H_0$ and $H_1$; (b) the degrees of freedom; (c) 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.