Parametric Tests for One GroupBy Ver Luanni F. Bilano, RPh

Hypothesis Testing for One Proportion

• Aim: to determine whether a sample comes from a standard population or norm which may:

a. be known through past experience

b. be specified as desired or claimed by the researcher

c. obey a basic law

Hypothesis Testing for One Proportion

• A survey was conducted among 200 randomly selected children to determine if the aim of the MHO to cover 80% of the target population was attained. It was found that 176 of the 200 (88%) children surveyed were immunized. Did the MHO meet his objective?

Hypothesis Testing for One Proportion

1. State Ho and Ha

Ho: P = 0.8

The proportion immunized in the target population is equal to 0.8 or 80%.

Ha: P ≠ 0.8

The proportion immunized in the target population is not equal to 0.8 or 80%.

Hypothesis Testing for One Proportion

2. State the level of significance

α = 0.05

3. Choose the test statistic

n

PQ

Ppz

n

PQ

Ppz

n

PQ

Ppz

Hypothesis Testing for One Proportion

4. Determine the critical region

z ≤ -1.96 OR z ≥ 1.96

Hypothesis Testing for One Proportion

5. Compute the test statistic

828.2

200

)2.0)(8.0(

8.088.0

88.0200

176

n

PQ

Ppz

p

Hypothesis Testing for One Proportion

6. Make a statistical decision

zc (2.828) > z0.05 (1.96)

Since the computed test statistic is within the C.R., reject Ho.

Hypothesis Testing for One Proportion

7. Draw the conclusion

The proportion immunized in the target population is not equal to 80%. It is significantly higher than 80%.

The MHO’s objective was achieved.

Hypothesis Testing for One Mean

Test statistic

– depends on whether or not the population variance (σ) is known

a. σ known:

b. σ unknown: df = n -1

n

xz

ns

xt

Hypothesis Testing for One Mean

A hospital director decided to shorten the waiting time of patients in the OPD to a mean duration of 25 minutes with a standard deviation of 2 minutes. After improvements were implemented, data collected from a random sample of 80 patients indicated a mean waiting time of 27.5 minutes. Does this result indicate that the goal of the hospital director was attained? (Use α = 0.05)

Hypothesis Testing for One Mean

In a sample of 49 adolescents who served as the subjects in an immunologic study, one variable of interest was the diameter of the skin test reaction to an antigen. The sample mean and standard deviation were 21 and 11 mm erythema respectively. Can it be concluded from these data that the population mean is less than 30? Let the level of significance be 5%.

Thank You!