Statistics Hypothesis

Test of Hypothesis

Objectives of the lesson

At the end of the lesson, the students should be able to:

• Distinguish the null hypothesis from the alternative hypothesis

• Determine whether to use z-test or t-test

• Determine the critical value and computed value of the test statistic

• Make a decision about the null hypothesis

Steps in Hypothesis Testing

STEP 1: State the null and alternative hypothesis

STEP 2: Determine the test statistic, significance level, and type of test ( left - tailed, right-tailed, or two-tailed )

STEP 3: Determine the critical value

STEP 4: Solve for the computed value ( test value )

STEP 5: Compare the computed and critical values then make a statistical decision whether to “reject” or “do not reject” the null hypothesis.

STEP 6: State the conclusion

Example # 1

The average salary of College Deans is at most Php 63,000. A sample of 35 College Deans has a mean salary of Php 65,700 with a standard deviation of  Php 5,250. At a = 0.01, test the claim that the College Deans earn more than Php 63,000 a month.

Multiple Choice

STEP 1: State Ho and Ha

• Ho: $$\mu$$ $$=$$ 63,000

  Ha: $$\mu$$ $$\ne$$ 63,000

• Ho: $$\mu$$ $$\ne$$ 63,000

  Ha: $$\mu$$ $$=$$ 63,000

• Ho: $$\mu$$ $$\ge$$ 63,000

  Ha: $$\mu$$ $$<$$ 63,000

• Ho: $$\mu$$ $$\le$$ 63,000

  Ha: $$\mu$$ $$>$$ 63,000

Multiple Choice

STEP 2: What is the test statistic that you should use?

• z - test

• t - test

Fill in the Blanks

STEP 2: What is the level of significance?

Multiple Choice

STEP 2: What is the type of test?

• Left-tailed test

• Right-tailed test

• Two-tailed test

Multiple Choice

STEP 3: Using your table, determine the critical value

• z_crit = 2.576

• z_crit = 2.326

• z_crit = 1.960

• z_crit = 1.645

Multiple Choice

STEP 4: Solve for z_comp

• z_comp = 3.041

• z_comp = 3.042

• z_comp = 3.043

• z_comp = 3.044

Multiple Choice

STEP 5: Decision Rule

• Reject Ho

• Do not reject Ho

Multiple Choice

STEP 6: Conclusion

• There is no enough evidence to support the claim that the monthly salary of college deans is more than PHP 63,000

• There is enough evidence to support the claim that the monthly salary of college deans is more than PHP 63,000

Example # 2

The mean age of the registered voters in a certain municipality is 35. A random sample of 35 registered voters from the same community has a mean age of 37 and the variance is known to be 36. The field reporter wants to prove that the record is not 35. Test the claim with 95% confidence level.

Multiple Choice

STEP 1: State Ho and Ha

• Ho: $$\mu$$ $$=$$ 35

  Ha: $$\mu$$ $$\ne$$ 35

• Ho: $$\mu$$ $$=$$ 37

  Ha: $$\mu$$ $$\ne$$ 37

• Ho: $$\mu$$ $$\ge$$ 35

  Ha: $$\mu$$ $$<$$ 35

• Ho: $$\mu$$ $$\le$$ 37

  Ha: $$\mu$$ $$>$$ 37

Multiple Choice

STEP 2: What is the test statistic that you should use?

• z - test

• t - test

Fill in the Blanks

STEP 2: What is the level of significance?

Multiple Choice

STEP 2: What is the type of test?

• Left-tailed test

• Right-tailed test

• Two-tailed test

Multiple Choice

STEP 3: Using your table, determine the critical value

• z_crit = 2.576

• z_crit = 2.326

• z_crit = 1.960

• z_crit = 1.645

Multiple Choice

STEP 4: Solve for z_comp

• z_comp = 1.975

• z_comp = 1.974

• z_comp = 1.973

• z_comp = 1.972

Multiple Choice

STEP 5: Decision Rule

• Reject Ho

• Do not reject Ho

Multiple Choice

STEP 6: Conclusion

• There is no enough evidence to support the claim that the mean age of registered voters is not 35

• There is enough evidence to support the claim that the mean age of registered voters is not 35