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CHAPTER 7 Notes

# CHAPTER 7 Notes - Chapter 6 CHAPTER 7 ESTIMATE NOW ITS YOUR...

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Chapter 6 CHAPTER 7: ESTIMATE NOW IT’S YOUR TURN Try question 7-2-17 first using your solutions manual as a guide and then try the following question . Remember that for the standard confidence levels, the z values are easily obtained by checking the bottom right corner of Table A-2. For your work you can use p and q without their “hats” and the check mark in the symbols program for your square root sign. Question 7-2-18. Given n=1200, x = 800, p = x/n, q = 1-p, 99 % confidence E = Z α /2 * ( ρ q/ n) = DETERMINING SAMPLE SIZE It is very important in research to know how many samples would be needed to be collected to approximate the estimated mean for a population. We do not want to collect less than 30 since the sample size is too small but we do not want to collect 300000000 samples since it may be too costly. In order to determine an adequate sample size we can use the formulas on page 352 of your text. One formula is used if we know the estimated population mean and the other formula is used if the population means (p and q) are unknown. Which ever formula is used, the answer must be rounded up to the next higher whole number since we cannot collect half a value. For example if n = 222.445, then we would collect 223 samples. 2 2 2 / ] [ E q p Z n α = is used if the p and q are known 2 2 2 / 25 . 0 ] [ E Z n α = is used if p and q are unknown TRY THESE PROBLEMS : Be sure to change all % values to decimals before you begin! Do you remember the secret to finding Z for standard confidence intervals? Do not forget to round up n. Question 7-2-25 Known values: 2 2 2 / 25 . 0 ] [ E Z n α = [(-1.96)^2 * 0.25] / (0.020)^2 = 2401 Question 7-2-26 Known values: 2 2 2 / 25 . 0 ] [ E Z n α = [(-2.575)^2 * 0.25] / (0.050)^2 = 664 Question 7-2-27 Known values: 2 2 2 / 25 . 0 ] [ E Z n α = [(-1.96)^2 * 0.27 * 0.73] / (0.030)^2 = 842 Question 7-2-28 Known values: 2 2 2 / 25 . 0 ] [ E Z n α = [(-1.645)^2 * 0.65 * 0.35] / (0.05)^2 = 247 1

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Chapter 6 7-3 ESTIMATING A POPULATION MEAN: σ KNOWN There are three ways of writing the estimate of the mean interval with its error: 1. E x E x + < < - μ 2. E x ± 3. ) , ( E x E x + - If we know the standard deviation, we can use the error formula: n Z E σ α = 2 / As you can see we are still using Z scores and Table A-2. The distribution should not have any extreme outliers The sample size (n) should be n > 30 As before, we can also determine the sample size needed: 2 2 / = E Z n σ α In order for these formulas to be used, all the necessary requirements, as outlined on pages 360-361, must be met. Read those pages and then finish the chart below. A. The population σ must be (known, unknown) B Sample size must be (n > 30, n 30) if distribution is abnormal C Distribution should be (absolutely, almost) normal. Question 7-3-9 Find the margin of error Confidence level % Sample size n Standard deviation σ α and α /2 Z α /2 n Z E σ α = 2 / Question 7-3-11 Find the margin of error Confidence level % Sample size n Standard deviation σ α and α /2 Z α /2 Copy the correct formula here n Z E σ α = 2 / Question 7-3-17 Find the sample size Confidence level % Error Standard deviation σ α and α /2 Z α /2 2
Chapter 6 2 2 / = E Z n σ α Question 7-3-19 Find the sample size Confidence level %

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