GIÁO TRÌNH MARKETING NGHIÊN CỨU - PHẦN 16 pot

Generalizing a Sample’s Findings to Its Population and Testing Hypotheses About Percents and Means Ch 16 2 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 parameters. Ch 16 3 Ch 16 4 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 5 Ch 16 6 How to Calculate Sample Error (Accuracy) n pq zerror = s p Where z = 1.96 (95%) or 2.58 (99%) Ch 16 7 Accuracy Levels for Different Sample Sizes • At 95% ( z = 1.96) • n p=50% p=70% p=90% • 10 ±31.0% ±28.4% ±18.6% • 100 ±9.8% ±9.0% ±5.9% • 250 ±6.2% ±5.7% ±3.7% • 500 ±4.4% ±4.0% ±2.6% • 1,000 ±3.1% ±2.8% ±1.9% The “p” you found in your sample 1.96 times s p 95% Confidence interval: p ± 1.96 times s p Ch 16 8 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 9 Parameter Estimation • Parameter estimation involves three values: 1. Sample statistic (mean or percentage generated from sample data) 2. Standard error (variance divided by sample size; formula for standard error of the mean and another formula for standard error of the percentage) 3. Confidence interval (gives us a range within which a sample statistic will fall if we were to repeat the study many times over Ch 16 10 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 [...]... - 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 Ch 16 +1.96 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?... statistic Ch 16 32 What is a Statistical Hypothesis? • A hypothesis is what someone expects (or hypothesizes) the population percent or the average to be • If your hypothesis is correct, it will fall in the confidence interval (known as supported) • If your hypothesis is incorrect, it will fall outside the confidence interval (known as not supported) Ch 16 33 How a Hypothesis Test Works • Sample Test hypothesis... the test Ch 16 29 Hypothesis Testing • Hypothesis: an expectation of what the population parameter value is • Hypothesis testing: a statistical procedure used to “accept” or “reject” the hypothesis based on sample information • Intuitive hypothesis testing: when someone uses something he or she has observed to see if it agrees with or refutes his or her belief about that topic Ch 16 30 Hypothesis Testing... Statistical hypothesis testing: – Begin with a statement about what you believe exists in the population – Draw a random sample and determine the sample statistic – Compare the statistic to the hypothesized parameter Ch 16 31 Hypothesis Testing • Statistical hypothesis testing: – Decide whether the sample supports the original hypothesis – If the sample does not support the hypothesis, revise the hypothesis... an upscale restaurant spend in restaurants per month (See p 465.) Ch 16 23 Parameter Estimation Using SPSS: Estimating a Mean • We must first use DATA, SELECT CASES to select LIKELY=5 • Then we run ANALYZE, COMPARE MEANS, ONE SAMPLE T-TEST • Note: You should only run this test when you have interval or ratio data Ch 16 24 Ch 16 25 Ch 16 26 Parameter Estimation Using SPSS: Estimating a Percentage • Estimating... Ch 16 11 Parameter Estimation • The lower the standard error, the more precisely our sample statistic will represent the population parameter Researchers have an opportunity for predetermining standard error when they calculate the sample size required to accurately estimate a parameter Recall Chapter 13 on sample size Ch 16 12 Standard Error of the Mean Ch 16 13 Standard Error of the Percentage Ch 16. .. confidence (z=1.96) • P=?%; q=100 %-? % p−z pq n Lower boundary Ch 16 p+z pq n Upper boundary 21 Estimating a Population Percentage with SPSS • How do we interpret the results? – Our best estimate of the population percentage that prefers “Rock” radio is 41.3 percent, and we are 95 percent confident that the true population value is between 36.5 and 46.1 percent Ch 16 22 Parameter Estimation Using SPSS:... 95%; corresponding to 1.96 standard errors Ch 16 15 Parameter Estimation • What does this mean? It means that we can say that if we did our study over 100 times, we can determine a range within which the sample statistic will fall 95 times out of 100 (95% level of confidence) This gives us confidence that the real population value falls within this range Ch 16 16 How do I interpret the confidence interval?... confidence interval range Ch 16 19 Parameter Estimation Using SPSS: Estimating a Percentage • Run FREQUENCIES (on RADPROG) and you find that 41.3% listen to “Rock” music • So, set p=41.3 and then q=58.7, n=400, 95%=1.96, calculate Sp • The answer is 36.5 %-4 6.1% • We are 95% confident that the true % of the population that listens to “Rock” falls between 36.5% and 46.1% (See p 464) Ch 16 20 sp = z How to Compute... samples 2.5% 2.5% • Plot the p’s • 95 % will fall in confidence interval 95% (p ± z times sp) Ch 16 17 Parameter Estimation • Five steps involved in computing confidence intervals for a mean or percentage: 1 Determine the sample statistic 2 Determine the variability in the sample for that statistic Ch 16 18 Parameter Estimation 3 Identify the sample size 4 Decide on the level of confidence 5 Perform . estimates of population parameters Ch 16 5 Ch 16 6 How to Calculate Sample Error (Accuracy) n pq zerror = s p Where z = 1.96 (95%) or 2.58 (99%) Ch 16 7 Accuracy Levels for Different Sample. estimate a parameter. Recall Chapter 13 on sample size. Ch 16 13 Standard Error of the Mean Ch 16 14 Standard Error of the Percentage Ch 16 15 Parameter Estimation • Confidence intervals: the. Generalizing a Sample’s Findings to Its Population and Testing Hypotheses About Percents and Means Ch 16 2 Statistics Versus Parameters • Statistics: values that are computed from