PRETEST

Directions: Choose the letter of the best answer. Write the chosen letter on a separate

sheet of paper.

1. In the estimation process, t-distribution is an appropriate statistical test use when ____.

A. the sample size is less than 30 B. the sample size is at least 30

C. the population mean is known D. the sample mean is known

2. What critical values correspond to degrees of freedom equal to 28 and 90%

confidence level?

A. t = 1.699 B. t = 2.048 C. t = 12.045 D. t = 17.01

3. Suppose that a one-tail t test is being applied to find out if the population mean is

less than 50. The level of significance is .05 and 25 observations were sampled. The

critical value of t is:

A. t = 1.708 B. t = 1.318 C. t = 1. 711 D. t = 1.316

4. Find the area under the t-distribution from t = -2.228 to t = 2.228 when n = 11.

A. 0.90 B. 0.95 C. 0.975 D. 0.995

5. Identify the percentile rank of the t-distribution when t = 1.699 and df = 29.

A. 90th B. 95th C. 97.5th D. 99.5th

LOOKING BACK

Before you proceed to this lesson, try to answer the question below to assess

what you have learned from the past lessons.

A group of 500 Grade 11 students took an achievement test. The scores have a

normal distribution, and the population mean and variance of the scores are 85 and

16, respectively. Determine the sampling distribution of the sample means of the

scores with a sample size of 100.

Activity 2

Find the area under the t-distribution from t = -2.060 to t = 2.060 when n = 26, then

illustrate the t-distribution.

CHECKING YOUR UNDERSTANDING

Directions: Show the step-by-step process in solving the following problems.

1. What are the critical values of t for area in two tails when the sample size is 24 with

confidence level of 98%?

2. Find the area to the left of critical value t = 2.500 when sample size is 24.

POST TEST

Directions: Choose the letter of the best answer.

1. Which of the following is true about the t-distribution?

A. A t-distribution is composed of bell-shaped curves. Each curve represents a

degree of freedom.

B. As the sample size decreases, the t-distribution approaches the standard

normal distribution.

C. The population is not normally distributed.

D. The distribution at the left of the mean is not the same as the distribution at

the right of the mean.

2. This table shows the probabilities/ areas of the t-distribution for different degrees of

freedom. This is used to find the critical values of t.

A. c-table B. d-table C. t-table D. z-table

3. What are the critical values of t when n = 25 and the confidence level = 90% in two

tails?

A. 2.064 B. 1.708 C. 1.318 D. 1.316

For nos. 4 and 5, refer to the given below.

Given df = 19 and t = -2.093

4. What is the area to the right of t = -2.093?

A. 90% B. 95% C. 97.5% D. 99%

5. What is the percentile rank of the critical value of t?

A. 0.05th B. 2.5th C. 97.5th D. 99.5th