MARKETING RESEARCH PART 16 pptx

Generalizing a Sample’s Findings to Its Population and Testing Hypotheses About Percents and Means Statistics Versus Parameters • Statistics: values that are computed from information provided by a sample • Parameters: values that are computed from a complete census which are considered to be precise and valid measures of the population • Parameters represent “what we wish to know” about a population Statistics are used to estimate population Ch 16 parameters Ch 16 The Concepts of Inference and Statistical Inference • Inference: drawing a conclusion based on some evidence • Statistical inference: a set of procedures in which the sample size and sample statistics are used to make estimates of population parameters Ch 16 Ch 16 How to Calculate Sample Error (Accuracy) error = z pq n Where z = 1.96 (95%) or 2.58 (99%) 2000 1850 1700 1550 1400 1250 1100 950 00 50 500 350 00 16% 14% 12% 10% 8% 6% 4% 2% 0% 50 sp Accuracy Sample Size and Accuracy Sample Size Ch 16 Accuracy Levels for Different Sample Sizes The “p” you found in your sample • At 95% ( z = 1.96) • n p=50% • • • • • 10 100 250 500 1,000 Ch 16 ±31.0% ±9.8% ±6.2% ±4.4% ±3.1% p=70% ±28.4% ±9.0% ±5.7% ±4.0% ±2.8% p=90% ±18.6% ±5.9% 1.96 times sp ±3.7% ±2.6% ±1.9% 95% Confidence interval: p ± 1.96 times sp Parameter Estimation • Parameter estimation: the process of using sample information to compute an interval that describes the range of values of a parameter such as the population mean or population percentage is likely to take on Ch 16 Parameter Estimation • Ch 16 Parameter estimation involves three values: Sample statistic (mean or percentage generated from sample data) Standard error (variance divided by sample size; formula for standard error of the mean and another formula for standard error of the percentage) Confidence interval (gives us a range within which a sample statistic will fall if we were to repeat the study many times over Parameter Estimation • Statistics are generated from sample data and are used to estimate population parameters • The sample statistic may be either a percentage, i.e., 12% of the respondents stated they were “very likely” to patronize a new, upscale restaurant OR • The sample statistic may be a mean, i.e., the average amount spent per month in restaurants is $185.00 Ch 16 10 How a Hypothesis Test Works • Sample Test hypothesis - Population • Exact amount Uses sample error • percent - Test against Ho • average - Test against Ho Ch 16 34 How to Test Statistical Hypothesis 2.5% 2.5% 95% +1.96 -1.96 Ch 16 35 Testing a Hypothesis of a Mean • Example in Text: Rex Reigen hypothesizes that college interns make $2,800 in commissions A survey shows $2,750 Does the survey sample statistic support or fail to support Rex’s hypothesis? (p 472) Ch 16 36 • Since 1.43 z falls between -1.96z and +1.96 z, we ACCEPT the hypothesis Ch 16 37 z How to Test Statistical p − Π Hypothesis = H s p − Π = pq n p H x − μH z= sx 2.5% = 2.5% x − μH s n 95% -1.96 Ch 16 Not Supported Supported +1.96 38 Not Supported • The probability that our sample mean of $2,800 came from a distribution of means around a population parameter of $2,750 is 95% Therefore, we accept Rex’s hypothesis Ch 16 39 Hypothesis Testing • Non-Directional hypotheses: hypotheses that not indicate the direction (greater than or less than) of a hypothesized value Ch 16 40 Hypothesis Testing • Directional hypotheses: hypotheses that indicate the direction in which you believe the population parameter falls relative to some target mean or percentage Ch 16 41 Using SPSS to Test Hypotheses About a Percentage • SPSS cannot test hypotheses about percentages; you must use the formula See p 475 Ch 16 42 Using SPSS to Test Hypotheses About a Mean • In the Hobbit’s Choice Case we want to test that those stating “very likely” to patronize an upscale restaurant are willing to pay an average of $18 per entrée • DATA, SELECT CASES, Likely=5 • ANALYZE, COMAPRE MEANS, ONE SAMPLE T TEST • ENTER 18 AS TEST VALUE • Note: z value is reported as t in output Ch 16 43 Ch 16 44 Ch 16 45 What if We Used a Directional Hypothesis? • Those stating “very likely” to patronize an upscale restaurant are willing to pay more than an average of $18 per entrée • Is the sign (- or +) in the hypothesized direction? For “more than” hypotheses it should be +; if not, reject Ch 16 46 What if We Used a Directional Hypothesis? • Since we are working with a direction, we are only concerned with one side of the normal distribution Therefore, we need to adjust the critical values We would accept this hypothesis if the z value computed is greater than +1.64 (95%) Ch 16 47 Ch 16 48 ... sample size Ch 16 12 Standard Error of the Mean Ch 16 13 Standard Error of the Percentage Ch 16 14 Parameter Estimation • Confidence intervals: the degree of accuracy desired by the researcher and... population parameters Ch 16 Ch 16 How to Calculate Sample Error (Accuracy) error = z pq n Where z = 1.96 (95%) or 2.58 (99%) 2000 1850 1700 1550 1400 1250 1100 950 00 50 500 350 00 16% 14% 12% 10% 8%... Ch 16 16 How I interpret the confidence interval? • Theoretical notion • Take many, many, many samples 2.5% 2.5% • Plot the p’s • 95 % will fall in confidence interval 95% (p ± z times sp) Ch 16