8.2 A Single Population Mean using the Student t Distribution
- Page ID
- 36501
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Section 8.2 A Single Population Mean using the Student t Distribution
Learning Objective:
In this section, you will:
- Apply and interpret point estimates and confidence intervals
- Construct and interpret confidence intervals for population means
Estimating a population mean (), when is NOT known
Critical Values - If is not known, instead of a normal distribution, we use a student t distribution to find the t-score. t/2 is the t-score that separates an area of /2 in the right tail of the student t distribution.
In addition to the t-score, we need to consider the degrees of freedom, n – 1. The number of degrees of freedom is abbreviated by df. df = n – 1.
Example 1: Find the critical value, t/2, for a sample size of 10, and corresponding to a 99% confidence level.
Calculating the confidence interval for population mean () when is NOT known
Using the Graphing calculator TI-84: STAT, TESTS, 8:TInterval (Data or Stats)
TInterval (Stats, 𝑥̅, 𝑠, 𝑛, CL) or Enter data L1, TInterval (Data, L1, 1, CL)
Example 2: Suppose you do a study of acupuncture to determine how effective it is in relieving pain.
You measure sensory rates for 15 subjects with the results given. Use the sample data to construct a 95% confidence interval for the mean sensory rate for the population (assumed normal) from which you took the data. 8.6; 9.4; 7.9; 6.8; 8.3; 7.3; 9.2; 9.6; 8.7; 11.4; 10.3; 5.4; 8.1; 5.5; 6.9
1
Notes 8.2
Example 3: A sample of 106 body temperatures has a mean of 98.2 degrees Fahrenheit a standard deviation of 0.62 degrees Fahrenheit. Construct a 95% confidence interval estimate of the mean body temperature of all healthy humans. Does the common use of 98.6 degrees Fahrenheit seem to a reasonable estimate of the mean body temperature?
For more information and examples see online textbook OpenStax Introductory Statistics pages 456-460.
“Introduction to Statistics” by OpenStax, used is licensed under a Creative Commons Attribution License 4.0 license