Question

A sample of 50 third-grade students had a average of 78 on a math proficiency test, with a sample standard deviation of 12. Is there enough evidence to conclude that the third-grade sample mean is different from the third-grade population mean of 67?

Assume a 0.02 significance level.

Use the Critical Value Method of Testing (this means NO P-Values!).

In your work space below, you will need to have -
1. The null hypothesis, Ho
2. The alternative hypothesis, H1
3. The test statistic
4. The type of test(left, right, two-tailed) and the critical value
5. The decision to accept Ho or reject Ho

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 67

H_a : 67

Test statistic = t

= ( - ) / s / n

= (78 - 67) / 12 / 50

Test statistic = 6.482

df = 49

Critical values are : -2.405 , +2.405

Reject the null hypothesis .