biometrics

All binomial variables are discrete random variables, but not all discrete random variables are binomial.

True

p = 0.5

Symmetric

p < 0.5

Skewed right

p > 0.5

Skewed left

Probability distributions represent theoretical populations.

True

Mean

Expected value

n

Number of trials

x

number of success

n-x

number of failures

p

probability of success

q

probability of failure

Assumptions for random variable

All observations are independent

Data result of chance events

Every outcome is mutually exclusive

Chi Square of Goodness of Fit Test

Could be used to compared observed numbers to expected numbers under a binomial distribution.

Probability distribution

Should add up to 1

What population parameters do you need to know to estimate the shape and spread of a binomial distribution?

Population mean (mu)

Standard deviation (sigma)

What statistical test would you use to determine if any observed discrete distribution follows the predicted distribution?

Chi Square Goodness of Fit Test

Normal Curve

Unimodal, symmetric, and bell-shaped.

Approximately 68% of observations lie between mean + or - 1 standard deviation regardless of the shape of the normal curve.

True

Normal Crive

mean = 0

standard deviation = 1

Binomial distribution is a probability distribution of the discrete random variable x.

True

If n*p > 5 you can use normal approximation for a binomial probability

True

If you have lots of observations for a continuous variable, you can smooth out the frequency histogram bars into a

Density curve

Sampling Error is an estimate of how much sample means from the same population could vary due to chance.

True

SDSM is theoretical.

True

Central Limit Theorem

The sampling distribution of means will approach a normal distribution as sample size increases.

Standard error is influenced by sample size. As n increases, the SE decreases.

True

As n increases it is more likely your sample mean will be close to the true population mean.

True

As n increases the standard error decreases.

True

Large samples more likely to have sample value close to the true population value.

True

As sample size increases, the standard deviation of the population sampled will decrease.

True

If a population is not normally distributed, the sampling distribution of sample means will appear normal if the sample size used is

Greater than 30

The standard error is equal to the standard deviation of the sampling distribution of sample means.

True

As sample size increases, there are 2 conceptual reasons that the spread of the SDSM gets smaller. What are they?

Impact of outliers is reduced and your sample has more information about population and so should have a value closer to true population value.

The sample mean is the point estimate used to estimate the population mean.

True

Sample value is a point estimate for a true population parameter.

True

Interval Estimate is a range of values you have “some confidence” includes the true population value.

True

The Sampling Distribution of Sample Means (SDSM) is the theoretical distribution of all possible means that could be sampled from a population.

True

The sample mean is an anchor in space but does NOT influence the interval size.

True

Interval Size is influenced by

• Level of confidence (1 - alpha) = z-value

• sample size

• variability

Alternative Hypothesis

Often the statement of interest because it says there IS a significant effect

If you reject the null hypothesis, then the probability of making a Type I error is less than alpha and will we report p<0.05.

True

If you do not reject the null hypothesis, then the probability we will report p>0.05.

True

What changes will usually increase power (all else equal)?

Increase sample size

Point estimates are single numbers and interval estimates are a range of values.

True

All else equal, a 95% confidence interval will have a larger interval length compared to a 90% confidence interval.

True

For a 95% interval, what are you 95% confident about?

The interval includes the true population value

Power is the ability to reject a Ho that is false.

True

When your sample data accurately reflects the true population values, what type of Correct Decision or Decisions were made when doing hypothesis testing?

Both Type A and Type B.

For every statistical test we have discussed so far, if we reject the null hypothesis, the probability of a type one error is less than 5%

True

You reject when z is greater than your critical value.

True

The t distribution is exactly equal to the z distribution when n>30.

True

What is the probability of a rare event?

p < 0.05