t-distribution

t-distribution

Poll

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Essential Question

How does estimation of parameters help in making conclusions drawn from a data of smaller sample sizes?

Learning Targets

• I can illustrate the t-distribution.

• I can identify percentiles using t-table.

• I can identify the length of a confidence interval.

• I can compute for the length of a confidence interval.

• I can compute for an appropriate sample size using the length of an interval

• I can solve problems involving sample size determination

The t-distribution is bell shaped and unimodal. It is symmetric about t=0. The t-distribution is used with small samples taken from population that is approximately normal.

t-distribution

How to find the t-score?

x̄ - sample mean
μ - population mean
s - standard deviation
n - sample size

Math Response

Given $$x̄=37$$ , $$\mu\ =32$$ $$s=9$$ and $$n=16$$

Type answer here

Correct Answer: 2.22

Deg^°

Rad

Math Response

Given $$x̄=68$$ , $$\mu\ =78$$ $$s=12$$ and $$n=9$$

Type answer here

Correct Answer: -2.5

Deg^°

Rad

Using the t-table.

To find a value in the Table of t-critical values, there is a need to adjust the sample size n by converting it to degrees of freedom df .

df = n-1

Math Response

What is the critical t-value given $$n=17$$ at 90% confidence level

Type answer here

Correct Answer: 1.75

Deg^°

Rad

Math Response

What is the critical t-value given $$n=21$$ at 95% confidence level

Type answer here

Correct Answer: 2.09

Deg^°

Rad

TRY THIS

A student researcher wants to determine whether the mean score in mathematics of the 25 students in Grade 8 is significantly different from the average of the school which is 89. The mean and the standard deviation of the scores of the students are 95 and 15, respectively. Assume 95% confidence level.