Reasons for taking a sample verses the whole population:

Time and Cost

Reasons for taking a sample versus the whole population:

Feasibility

Sometimes it's not possible to survey the population, so taking a sample is the only option.

(determining the winner of an election)

Reasons for taking a sample versus the whole population:

Accuracy

Types of samples:

Non probability sample

A sample in which the items have unknown probabilities of being selected.

(Convenience sample)

Types of samples:

Probability Sample

Sample in which items are selected based upon known probabilities.

(Simple random sample)

***Probability sampling is necessary when making an inference. 

The error incurred by taking a sample instead of a census. 

(When you look at anything less than the entire population, you are not going to report with 100% accuracy)

Error incurred when some subjects refuse to respond to a survey.

(Estimating percentage of car crashes involving alcohol. Drunk drivers usually refuse BAC test.)

When data collected does not reflect the true measures. 

(When you don't give honest answers, skews results)

The set of all possible statistics could be represented by a histogram, or distribution.

This distribution is referred to as a sampling distribution. The sampling distribution has it's own mean and standard deviation. 

Major goal of inferential statistics: To make conclusions about the population based upon a single sample. 

If the population is not normal then the shape of the sampling distribution is normal for large samples (n>30).

Also, as the sample size (n) increases, the sampling distribution will become more normal.

Hypothesis Errors:

Type 1

Hypothesis Error

Type 2

What are elements of inferential statistical problems?

a.    calculating a sample mean

b.    selecting a probability sample

c.    estimating a population parameter

the distribution is approximately normal with a mean of 10

                  minutes and a standard error of 0.8 minutes

The probability distribution of all possible values of the sample

mean  x is

the sampling distribution of  x

The mean of the sampling distribution of x is equal to

the mean of the population

Whenever the population has a  probability distribution of nonnormal shape, the sampling distribution of x is a normal probability distribution

for only sample sizes of 30 or greater

Whenever the population has a  probability distribution of nonnormal shape, the sampling distribution of p is a normal probability distribution

for the situation where both  np  and   n(1-p) are at least 5    

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample means whenever the sample size is large is known as the

central limit theorem

As the sample size decreases, the

the standard error of the mean increases

The hypothesis tentatively assumed to be  true is

the null hypothesis

The probability of making a Type I error is the probability of

rejecting a true null hypothesis 

In the past, the average grade on the final examination in

statistics is at least 85.  A student taking the final thought that the

final was hard and plans on taking a sample to test her belief that

the average score has decreased.  The correct set of hypotheses is

H_o:  u >   85     versus      H_a:  u  <  85

What's true regarding the p value and it's effect on the sample evidence?

the smaller the p-value, the stronger the sample evidence is

         to reject

Suppose your test statistic is 2.35 and your critical values are

         ±  2.10.  Your conclusion is 

a.             There is evidence that the average idle time per day for all construction workers is different than 72.