Chapter 1 Review

quantitative variable

is one that is expressed with a meaningful number. ex Temperature, income, age, diameter

qualitative variable

is one that is not expressed with a meaningful number, like brand of automobile, sex, hair color, and state of residence

4 measurement levels

Nominal, Ordinal, Interval, and Ratio

Nominal

items are grouped, but no order is implied
ex. sex, ethnicity

Ordinal

items are grouped and there is order to the groups, but distance between each grouping is not necessarily the same.
ex. birth order and your level of pain on scale of 1 to 10

Interval

items are grouped, there is order to the groups, the distance between the groups is the same, but the zero point is arbitrary
ex. SAT scores, time

Ratio

items are grouped, there is order to the groups, the distance between the groups is

the same, and the zero point is meaningful
ex. income, age, distance

Greek vs Latin letters

Use greek letters for population
latin letters for sample

Central Limit Theorem

If I take all possible samples of size   from a population, and compute   for each sample, and then organize all of those means into a probability distribution, we obtain the “sampling distribution of the sample mean

• The mean of all the sample means will equal the population mean

• If the sample size is sufficiently large (30), the sampling distribution will be normally distributed

Sampling Distribution Characteristics

• The mean of the sampling distribution is the same as the mean of the population.

  • Standard error of the mean = population standard deviation / square root of sample size

Empirical Rule

In the sampling distribution for the sample mean…

“population mean +- 1(population standard deviation) / square root of population size” will contain 68.26% of all sample means

“population mean +- 2(population standard deviation) / square root of population size” will have 95.44%,

“population mean +- 3(population standard deviation) / square root of population size” will have 99.74%

Z-score

how many standard deviations a specific data point lies above or below the mean of a dataset

Alternative Hypothesis

The test you want to prove

Null hypothesis

The one we test.

The equal sign ALWAYS goes in the null hypothesis

If the p-value is low, reject the null

P-value

the actual chance of committing a type I error if you reject the null hypothesis
if the 𝑝-value is less than our level of significance, 𝛼, we reject the null

hypothesis

Type I error

actual state of nature is True but researcher’s decision is to reject the null hypothesis
(false positive that rejects a true null hypothesis)

Type II error

actual state of nature is false, but researchers decision is to fail to reject the null hypothesis
(false negative that fails to reject a false null hypothesis)

Steps to testing hypotheses

1. Develop your null and alternative hypotheses

2. Specify the level of significance

3. Collect the sample data and compute the value of the test statistic

4. Compute the  p-value from the test statistic

5. Compare the  p-value to the level of significance

6. Interpret the statistical conclusion in the context of the problem; be able to tell the story

formula to find t value (aka t statistic)

test statistic = sample mean - population mean / (sample standard deviation / square root of sample size)

What is a t statistic (aka t value)

measures the size of the difference between your sample data and your expected or null hypothesis value, relative to the amount of variation (or standard error) in your data

Degrees of freedom

n - 1

sample size - 1