Question

A high school math teacher claims that students in her class will score higher on the math portion of the ACT then students in a colleague’s math class. The mean ACT math score for 49 students in her class is 22.1 and the standard deviation is 4.8. The mean ACT math score for 44 of the colleague’s students is 19.8 and the standard deviation is 5.4. At α = 0.05, can the teacher’s claim be supported?

a. Write down the type of test you will conduct.

b. Write down the null and alternative hypotheses.

c. Construct the test statistic.

d. Conduct the test.

e. What do you conclude?

Answer 1

Ans:

a)Independent samples t test

b)

c)

pooled standard deviation=SQRT(((49-1)*4.8^2+(44-1)*5.4^2)/(49+44-2))=5.0923

standard error for difference=5.0923*SQRT((1/49)+(1/44)=1.0576

Test statistic:

t=(22.1-19.8)/1.0576

t=2.175

d)

df=49+44-2=91

p-value=tdist(2.175,91,1)=0.0161

As,p-value<0.05,we reject the null hypothesis.

e)

There is sufficient evidence to support the teacher's claim that students in her class will score higher on the math portion of the ACT then students in a colleague’s math class.