Marketing 4202 Final Exam Review Covering chapters 8 14 15 16 17 19 And sessions 11 16 Session 11 Review of statistics part 2 inferential statistics Chapters 14 16 In class case Exporting jeans to the Netherlands MDP Should we export high end jeans to the Netherlands Because they re so tall should we export large sized jeans This may cause major changes in the production process MRP Obtain information on length of Dutch men What is the proportion of customers that are taller than XX inches Determine other demographic characteristics in particular about income The three fundamental distributions in statistics 1 Population distribution Frequency distribution histogram of the population elements for a certain variable height or income generally a smooth line it is unknown mean of population distribution is mu and standard deviation is 2 Sample distribution Frequency distribution histogram of the sample elements for example height known once we have our sample mean of the sample distribution is the sample mean X bar and standard deviation is S 3 Sampling distribution Distribution histogram of all possible sample means X bar you could get it is theoretical distribution a Take many samples from a population b compute x bar for each sample and then c construct a frequency distribution histogram from all computed sample means when sample size to compute the sample means is large sampling distribution is a normal distribution bell shaped with mean mu standard deviation S sq rt Of n this result is the Central Limit theorem The sampling distribution is the theoretical foundation for confidence intervals and hypothesis testing If your sampling distribution is fat s sq rt N is large sample mean is far from the mu If your sampling distribution is skinny s sq rt N is small sample mean is likely to be closer to mu Confidence interval Tells you how large the random error is and is more informative than a point estimate To estimate population mean use sample mean X bar will not be exactly equal to mu so x bar mu random sampling error To compute confidence interval for the mean use the formula For a 95 confidence interval Z confidence corresponds to 95 area under the standard normal curve Confidence interval interpretation In the long run 90 of the confidence intervals constructed in the same way as before will contain the true value mu or we are 90 sure that the interval contains the true population mean for Testing a hypothesis about a population mean 1 Formulate the null and alternative hypothesis a Null what you want to test specifies that population mean mu is equal to a single value Ho Mu b Alternative states that the population mean is different from the value specified in the null Ha Mu doesn t 2 Choose the significance level 3 Compute the test statistic a Measures how close the sample has come to the null Should follow a well known distribution such as the normal t or chi square distribution 4 Prepare a statistical decision p value a When is Z test too large that I do not believe anymore that the null is true confidence interval If null is true then frequency distribution is a standard normal distribution b P Value The probability of observing a value for Z test that is at least as contradictory to the null as the one actually computed 5 Make a statistical decision reject or not reject the null a Compare P value to significance level Significance level is the critical probability in choosing between the null hypothesis and the alternative hypothesis usually 1 5 or 10 If P Value is less REJECT if P Value is more DO NOT REJECT 6 Make a managerial decision interpretation Session 12 Frequency tables and cross tabs for nominal and ordinal data Part 1 Chapters 15 16 Inferential statistics for population proportions Sample proportions p are used to infer about population proportions pi Testing a hypothesis about population proportions 1 Formulate a null and alternative hypothesis a For nominal and ordinal data these are stated in terms of population proportions 2 Choose the significance level a Significance level is the critical probability in choosing between the null and alternative hypothesis When P Value is less that Sig level REJECT and when it is larger DO NOT REJECT 3 Compute the test statistic hypothesis a Test statistic measures how close the sample has come to the null b For testing about a proportions from a frequency table use Chi Squared test stat 4 Prepare a statistical decision P Value a When X 2 is small your data is close to the null and when it is b large it is far away from the null If null is true frequency distribution of all possible x 2 values is a chi squared distribution 5 Make a statistical decision reject or not reject the null 6 Make a managerial decision interpretation Session 13 Frequency tables and cross tabs for nominal and ordinal data Part 2 Chapters 15 16 Descriptive technique Cross tabulation A frequency distribution describes one nominal ordinal variable at a time while a cross tabulation describes two nominal ordinal variables simultaneously We call this bivariate statistical analysis the statistical investigation of the relationship between two variables A cross table can be seen as the merger of two frequency tables it is probably the most widely used statistical technique in MR because it is easy to understand and simple to conduct Cross tabulation Freq table 1 Freq table 2 Computing percentages in cross tables Percentages facilitate interpretation You need to find out whether you compute percentages row wise or column wise Step one Find out what the research question is i e what groups does the manager client want to compare EX Are firms of different acct sizes equally likely to recommend the company or are smaller accts more likely to recommend than larger ones Step two Look at the cross tab and decide whether you are comparing columns or rows EX We want to compare columns different account sizes Step three Compute the percentages as follows If you want to compare the columns Compute column percentages If you want to compare the rows Compute row percentages What is the conclusion It seems that customers that have different account sizes have different response patterns towards recommendation Firms with small accounts are less negative about recommending the company than firms with large accounts Statistical question Have these differences occurred because of chance in this one sample or are these likely reflecting real differences in the population