MRKT 345 Midterm Exam Chapters 8-11

What are Sample Statistics?

-A summary description of a variable of the sample, hence is computed from the data -The sample statistic is used as an estimate for the population parameter -Roman letters for notation, e.g. X bar or S

What are population parameters?

-A summary descriptions of variables of the population -This parameter denotes the 'true value' from a census ('total population') rather than a smaple -Greek letters as notation, e.g. mu or theta

Normal Distribution

-Bell shaped and symmetric -Fully described by its mean and standard deviation -Easy to compute probability once you know mean and standard deviation

Sample Distribution

-Frequency distribution (histogram of sample elements (is constructed from our sample) -Is generally not so smooth, but will looks like the population distribution -The mean of the sample distribution is the sample mean X bar -The st. dev. of the sample distribution is S

The alternative hypothesis

-Is also a statement about the population mean Mu -It states that the population mean is different from the value specified under the null hypothesis

Numerical Summaries acceptable for nominal and ordinal scales

-Proportions (=%), counts, or frequency tables

Descriptive Statistics

-Techniques to describe results from a survey

Sampling distribution

-The distribution (histogram) of the sample means (X bar) -A Theoretical distribution -When the sample size to compute the sample means is large, the sampling distribution is a normal distribution (bell shaped)

The null hypothesis

-The hypothesis you wish to test -It specifies that the population mean Mu is equal to a single value -It usually follows from your problem definition, from the decision maker (manager) or from 'the current norm'

Measures for Dispersion

-Variance: Avg. Squared difference -Standard Dev: Square Root of Variance -Range: Largest Value- Smallest value

Hypothesis testing is to ....

use a sample to prove or disprove a brief about the population

6 steps to Testing a Hypothesis

1) Formulate the null and alternative hypotheses 2) Choose the significance level 3) Compute the test-statistic 4) Prepare a statistical decision (P-Value) 5) Make a statistical decision: reject or the null hypothesis 6) Make a managerial decision/interpretation

Research hypothesis

An unproven statement or proposition about a phenomenon of interest

If the p-value is LARGER than alpha: ______ the null hypothesis

DO NOT REJECT

Population distribution

Frequency distribution (histogram) of the population, usually a smooth line, but it unknown

descriptive statistics ideal for nominal and ordinal

Frequency tables, bar chart, or pie chart

Population parameters are denoted by ______ _____ and are also ______ to the researcher.

Greek letters, unknown

The target population is represented by _________ ________, while samples are represented by ______ _______

Inferential statistics, descriptive statistics

Numerical summaries for interval and ratio scales

Mean, median, std. dev., variance, or range

Test-Statistic

Measures how 'close' the sample has come to the null hypothesis

Population Parameter

Mu (greek)

You ______ accept a null hypothesis

NEVER

Can you report means, std. dev. for nominal and ordinal variables?

NO SIR

If the p-value is LESS than alpha: ______ the null hypothesis

REJECT

Research Questions

Refined statements of the specific components of the problem

If the null hypothesis is true than the frequency distribution of all possible Z values is a _____ ______ ______

Standard normal distribution

Inferential Statistics

Techniques to generalize the results from the sample to a larger population- we'll never be able to know the 'exact truth' but can make a good educated guess about it using inferential statistics

Confidence Interval

Tells you how large the random error is, and it is more informative than a point estimate

What is the significance level of the test?

The critical probability in choosing between the null hypothesis and the alternative hypothesis

Statistical inference in MR

We want to know things about 'the population', especially about the population distribution of one or more variables

Sample Parameter

X bar (roman)

Descriptive statistics ideal for interval and ratio

histogram

Marketing researchers _____ about the population distribution and the population parameters using a ________.

learn, sample

Line charts are useful for analyzing _______ _______ ___ _____ _____ _____ ______

longitudinal measurements at several points over time

Numerical Descriptive Statistics

numerical summaries of data (ex. central tendency (mean, median, mode), measures of dispersion (standard dev., variance, range)