Within a school district, students were randomly assigned to one of two Math tea

Question

Within a school district, students were randomly assigned to one of two Math teachers - Mrs. Smith and Mrs. Jones. After the assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25 students. At the end of the year, each class took the same standardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10; and Mrs. Jones' students had an average test score of 85, with a standard deviation of IS. Assume the variances are equal. At the significance level 0.10, can we conclude that Mrs. Jones is a more effective teacher than Mrs. Smith? a). Calculate the test statistic. (R code and R result). b). Find the p-value (R code and R result). c). Make (type) your decision.

Explanation / Answer

Solution:-

By using R-software

To test,

> cat("Ho:mu1=mu2 H1:mu1< mu2 ")
Ho:mu1=mu2 H1:mu1< mu2

(a)

> n1=30;n2=254;xb1=78;xb2=85;v1=10^2;v2=15^2;
> n=n1+n2-2
> n
[1] 282
> sp=sqrt((n1*v1+n2*v2)/(n1+n2-2))
> sp
[1] 14.60472
> to=(xb1-xb2)/(sp*sqrt(1/n1+1/n2))
> to
[1] -2.482693

(b)

> pv=pt(to,n,lower.tail=F)
> pv
[1] 0.9931894

(c)

> cat("computed value of t = ",to, " ") >cat("degree of freedom=",n1+n2-2, " ")
computed value of t = -2.482693
degree of freedom= 282
logical(0)
> cat("p-value = ",pv," ")
p-value = 0.9931894
> cat("Conclusion :If level of significance < ",pv,"accept Ho ")
Conclusion :If level of significance < 0.9931894 accept Ho
> cat("Otherwise accept Ho ")
Otherwise reject Ho

Here, We accept Ho ,therefore we conclude that Mrs. Jonnes and Mrs. Smith are equally effective teachers.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

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