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)