A school district is considering going to a 12-month schedule, with students att

Question

A school district is considering going to a 12-month schedule, with students attending school for three 3-month periods with a break of one month between trimesters. A sample of 209 of the school district's parents was conducted. The response were categorized as to (1) number of children in the family and (2) option on the new schedule. The results are summarized below. We would like to do chi-square test to see if opinion is independent of number of children. How many degrees of freedom would be appropriate? We would like to conduct a chi-square test to see if the number of children is independent of the opinion. To conduct this test we will need the expected values. The expected value for the cell with 1 child and favoring the program would be?

Explanation / Answer

Null HYpothesis : H0 : Opinion is independent of number of children.

Alternative HYpothesis : Ha : Opinion is dependent on number of children.

Observed Table

Expected value

(i) 1 child and favouring the program = Total 1 number of children * Total favoured person/ Total people

= 82 * 99/ 209 = 38.84

similarly, expected table

Degree of freedom = (3 -1) * (3-1) = 4

HEre value of chi - square

X2 = (0i - Ei )2 / Ei

The value of X2 = 51.515

and dF = 4 and alpha = 0.05

X2 cr = 9.488

so here X2 > X2 cr

so we will reject the null hypothesis and conclude that Opinion is dependent on number of children.

Number of Children Favor Undecided Opposed Total 1 16 24 59 99 2 29 10 11 50 3 or more 37 15 8 60 total 82 49 78 209

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.