Does a new math program improve student performance? A random sample of 20 stude

Question

Does a new math program improve student performance? A random sample of 20 students was taken from students using a new algebra textbook emphasizing group work and a second sample of 30 students was taken from students using a more traditional textbook. The observations from the end of the course are in the table below. Conduct a goodness of fit test using Minitab to determine if the proportions from each group are equal at each performance level. Answer the question using the five step hypothesis process and provide your supporting Minitab output.

Explanation / Answer

Here we have to test the hypothesis that,

H0 : Grade level and text are independent.

H1 : Grade level and text are not independent.

Assume alpha = level of significance = 5% = 0.05

The test statistic is,

X2 = (O - E)2 / E

where O is observed frequency and

E is the expected frequency.

We can fidn E by using forluma,

E = (Row total)*(column total) / sample size

Expected frequency for 8,

E = (14*20) / 50 = 5.6

Expected frequency for 6,

E = (21*20) / 50 = 8.4

Expected frequency for 6,

E = (15*20) / 50 = 6

Expected frequency for 6,

E = (14*30) / 50 = 8.4

Expected frequency for 15,

E = (21*30) / 50 = 12.6

Expected frequency for 9,

E = (15*30) / 50 = 9

The table of observed and expected frequency is,

Test statistic X2 = 2.8571

For taking decision we have to find P-value.

P-value we can find by using EXCEL.

syntax is,

=CHIDIST(x, deg_freedom)

where x is test statistic value.

deg_freedom = (R-1)*(C-1)

where R is number of rows = 2

C is number of columns = 3

deg_freedom = (2-1) * (3-1) = 1*2 = 2

P-value = 0.24

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Grade level and text are independent.

O E (O-E)^2 (O-E)^2/E 8 5.6 5.76 1.028571 6 8.4 5.76 0.685714 6 6 0 0 6 8.4 5.76 0.685714 15 12.6 5.76 0.457143 9 9 0 0 total 2.857143

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

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