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

This is the seventeenth page of the series of free video lessons, “Statistics Lectures”. 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.

**Related Pages**

15: Sampling Error & Central Limit Theorem

16: Sample Proportions & Confidence Intervals 1

18: Hypothesis Testing

19: Effect Size, Power, Statistical vs. Practical Significance

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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.

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.

Two requirements for constructing meaningful confidence intervals about the population proportion:

- The size of your sample is no more than 5% of the size of the population it was drawn from.
- np(1-p) ≥ 10

If the sample meets this requirement, it means that it has an approximately normal distribution.

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.

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