 # Statistics Lectures - 17

A series of free Statistics Lectures with examples & solutions in videos.

These lectures cover the concepts of t-distribution, confidence intervals about the mean, population standard deviation, confidence intervals for population proportions and calculating required sample size to estimate population proportions.

This is page seventeen of the series of free video lessons, "Statistics Lectures".

### Statistics - Lecture 48

Student's t-Distribution
When performing any type of test or analysis using a Z-score, it is required that the population standard deviation is already known.
The degrees of freedom change how the probability distribution looks. The probability distribution of t has more dispersion than the normal probability distribution associated with t.

### Statistics - Lecture 49

Confidence Intervals about the Mean, Population Standard Deviation Unknown
We construct confidence level to help estimate what the actual value of the unknown population mean is.
Example:
On the Verbal Section of the SAT, a sample of 25 test-takers has a mean of 520 with a standard deviation of 80. Construct a 95% confidence about the mean.

### Statistics - Lecture 50

Confidence Intervals for Population Proportions
Two requirements for constructing meaningful confidence intervals about the population proportion:
1. The size of your sample is no more than 5% of the size of the population it was drawn from.
2. np(1-p) ≥ 10
If the sample meets this requirement, it means that it has an approximately normal distribution.

### Statistics - Lecture 51

Calculating Required Sample Size to Estimate Population Proportions
Example:
In a recent poll of 200 households, it was found that 152 households had at least one computer. Estimate the proportion of households in the population that have at least one computer. Construct a 95% confidence interval to estimate the population proportion.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 