Samples, proportions, and confidence intervals - L7

What should the distribution of sample proportions be about the population proportion?

Normally distributed

What is the distribution of sample proportions affected by?

Sample size - the larger the sample size, the closer the sample proportion to the population proportion

What is the equation for standard error of a mean?

Standard error = standard deviation/sqrt sample size

What is the equation for standard error of a proportion?

Standard error = sqrt (population proportion x [1 - population proportion]/n)

How is population proportion estimated?

As long as the sample size is reasonable (>30), the sample is a reasonable estimate of population proportion

What are the 2 common thresholds used for rejecting the null hypothesis?

5% and 1% (alpha = 0.05 or alpha = 0.01)

If a population parameter (such as population mean or proportion) is unknown, what is it estimated from?

The sample, but the sample must have been randomly selected

Why is an estimate of a population mean called a point estimate?

Because samples are being used

What can be done to give greater confidence that the sample mean is a good estimate of the population mean?

An interval estimate called a confidence interval can be calculated

What is a confidence interval?

An interval for which, with a certain level of confidence, the value estimated lies between 2 values

What value of confidence intervals are commonly used?

95% and 99%

How do you establish if there is no significant difference when comparing mean values of 2 different groups?

If either of the upper or lower limit of the confidence interval of one mean overlaps with the confidence interval of the other mean, there is no significant difference

What does a hi-lo plot show?

The confidence intervals of means to see if they overlap or not

What is the equation for calculating a 95% confidence interval for sample means?

95% CI = sample mean ± 1.96 x (standard deviation/sqrt number of units)

What is the equation for calculating a 99% confidence interval for sample means?

99% CI = ± 2.58 x (standard deviation/sqrt number of units)

What is the equation for calculating a 95% confidence interval for proportions?

95% CI = proportion ± 1.96 x sqrt(p[1-p]/n)

What is the equation for calculating a 99% confidence interval for proportions?

99% CI = proportion ± 2.58 x sqrt(p[1-p]/n)

When can sample standard deviation be used as a reasonable estimate of population standard deviation?

• Data is normally distributed

OR

• Sample size is larger than 30