Question

The mean class grade for all health sciences statistics students from previous semesters was 85% with a standard deviation of 7%. We want to know if the current class of statistics students is significantly different from the previous years’ population. The current mean class grade is 87% with a standard deviation of 5%. There are 30 students in the class. Use α = .10.

a. What is the SEM?

b. What is the critical value?

c. What is the one-sample z-test test statistic?

d. Is this finding statistically significant? Why or why not?

e. What is Cohen’s D?

Answer 1

Solution-:A:

SEM=stndard error of mean=sigma/sqrt(n)=7/sqrt(30)=1.278

b. What is the critical value?

alpha=0.01

alpha/2=0.01/2=0.005

In excel:

=NORM.INV(0.005,0,1)

=2,57583

Z>2.57583

Critical z=2.57583

c. What is the one-sample z-test test statistic?

z=xbar-mu/sigma/sqrt(n)

=(87-85)/(7/sqrt(30))

= 1.5649

ztest statistic,z= 1.5649

Solution-d:

Ho:mu=85

Ha:mu not =85

alpha=0.01

z=1.5649

z crit=2.57583

z<Zcrit

1.5649<2.57583

Fail to reject Ho

Accept Ho

There is no sufficient statistical evidence at 5% level o ff significance to conclude that current class of statistics students is significantly different from the previous years’ population

Not statistcally significant.

e. What is Cohen’s D?

Cohen'D=xbar-mu/sigma

=87-85/7

= 0.28571