Question

test the hypothesis of independence. can you conclude that opinion and household size are not independent? use the α = 0.05 level of significance and the p - value method with the ti - 84 plus calculator. (a) state the null and alternate hypotheses. h0: household size and opinion are independent. h1: household size and opinion are not independent. part 1 of 7 (b) compute the value of the test statistic. round the answer to three decimal places. χ2 = part 2 of 7

Explanation:

Step1: State hypotheses

The null hypothesis $H_0$ is that household size and opinion are independent. The alternative hypothesis $H_1$ is that household size and opinion are not independent. So, $H_0$: Household size and opinion are independent; $H_1$: Household size and opinion are not independent.

Step2: Compute test - statistic (general formula)

The test - statistic for a test of independence is $\chi^{2}=\sum\frac{(O - E)^{2}}{E}$, where $O$ is the observed frequency and $E$ is the expected frequency. However, since we are asked to use a TI - 84 Plus calculator, we would input the contingency - table data into the calculator. First, we enter the data into a matrix (e.g., a 2 - way table). Then, we use the STAT $
ightarrow$ `TESTS` $
ightarrow$ C:χ2 - Test function on the TI - 84 Plus. But without the actual contingency - table data, we cannot perform the numerical calculation.

Answer:

(a) $H_0$: Household size and opinion are independent; $H_1$: Household size and opinion are not independent.
(b) Cannot be computed without contingency - table data.