Question

Edith Educationer is analyzing the test scores for Calculus students taught using two different methods: a traditional method, and a web-based, self-paced method.  She feels that the traditional method is better suited for teaching Calculus.  Run a hypothesis test at α = 0.05, to determine if the test scores in the traditional method are higher.

Conduct a hypothesis test, using the traditional method, and provide all 5 steps to your hypothesis test.

Traditional Web-based, Self-paced

Mean Test Score X₁=87 X₂=80

Population Variance   σ ^2₁=26 σ ²₂ = 35

Sample Size 50 40

Answer 1

Answer)

1)

Null hypothesis Ho : u 1 = u 2

Alternate hypothesis Ha : u1 > u2

2)

Test statistics is = (x1-x2)/standard error

Standard error = √{(v1/n1)+(v2/n2)}

Where v1 =26, v2 = 35

N1 = 50, N2 = 40

After substitution

Test statistics z is = 5.93

3)

Now as the population variances are known here, we can use standard normal z table to estimate the critical value and the rejection region

Alpha = 0.05

From z table, P(z>1.645) = 0.05

So, critical value is 1.645

Now rejection region is

If calculated test statistics is greater than 1.645 reject Ho (null)

4)

As 5.93 > 1.645

Reject Ho

5)

We have enough evidence to support the claim that scores are greater in traditional