Solutions%20for%20Problems%20of%20Chapter%208%20Estimating%20Single%20Population%20Parameters

# Solutions%20for%20Problems%20of%20Chapter%208%20Estimating%20Single%20Population%20Parameters

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Unformatted text preview: Chapter 8 Estimating Single Population Parameters When applicable, selected problems in each section will be done following the appropriate step-by-step procedures outlined in the corresponding sections of the chapter. Other problems will provide key points and the answers to the questions, but all answers can be arrived at using the appropriate steps. The more difficult problems in this chapter are: For Section 8.1 8.11, 8.18, 8.19, 8.20, 8.25, 8.26 For Section 8.2 8.32, 8.33, 8.34, 8.41, 8.42, 8.43, 8.44, 8.45 For Section 8.3 8.55, 8.64, 8.65, 8.69, 8.70 For End of Chapter 8.79, 8.80, 8.85 Section 8-1 Exercises 8.1. Since the population standard deviation is unknown, the following steps can be used to compute the confidence interval estimate. Step 1: Define the population of interest and select a simple random sample. The population of interest is the collection of all items of interest. A simple random sample of size n = 13 will be collected. Step 2: Specify the confidence level. The desired confidence level is 95%. Step 3: Compute the sample mean and the sample standard deviation. The sample mean and sample standard deviation are given to be: 18.4 x = 4.2 s = Step 4: Determine the standard error of the sampling distribution. The sample standard deviation is computed to be 4.2 s = . The standard error of the sampling distribution is: 4.2 1.16 13 x s n σ ≈ = = Step 5: Determine the critical value for the desired confidence level. The critical value for 95% confidence from the student t-distribution table with degrees of freedom equal to n – 1 = 12 is t = 2.1788. Step 6: Compute the confidence interval estimate. The 95% confidence interval estimate for the population mean is: s x t n ± Therefore the confidence interval is: 4.2 18.4 2.1788 13 ± 18.4 2.54 ± 15.86 --------------------------------- 20.94 234 Chapter 8 | Estimating Single Population Parameters 8.2. The 90% confidence interval estimate for the population mean is: x z n σ ± The critical value for 90% confidence from the standard normal distribution table is z = 1.645. Therefore the confidence interval is: 70 + 1.645(1.86) 70 + 3.06 66.94 ---------------------------------73.06 8.3. Since the population standard deviation is known, the following steps can be used to develop the desired confidence interval estimate. Step 1: Define the population of interest and select a simple random sample. The population of interest is the collection of all items of interest. A simple random sample of size n = 250 will be collected. Step 2: Specify the confidence level. The desired confidence level is 95%. Step 3: Compute the sample mean. The sample mean is given to be 300 x = . Step 4: Determine the standard error of the sampling distribution....
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Solutions%20for%20Problems%20of%20Chapter%208%20Estimating%20Single%20Population%20Parameters

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