Sample sizes and confidence intervals for proportions Chong Chun Wie Ext: 2768 ChongChunWie@imu.edu.my Content • Sampling distribution of sample means (SDSM) • Normality Test • Estimating a population mean: σ known • Estimating a population mean: σ unknown • Standard deviation of proportion • Confidence interval of proportion • Hypothesis testing with proportion Population and Sample Samples Populations Sampling distribution of sample means (SDSM) Sampling distribution • Example – Select
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confidence intervals The confidence intervals represent upper and lower bounds of variation around each reference forecast. Values may occur outside the confidence intervals due to external shocks‚ such as extreme weather‚ structural changes to the economic system‚ geopolitical events‚ or technology development. The confidence intervals increase in width throughout the forecast period due to the increasing level of uncertainty in each subsequent year. The upper and lower bounds were based
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Confidence Intervals Consider the following question: someone takes a sample from a population and finds both the sample mean and the sample standard deviation. What can he learn from this sample mean about the population mean? This is an important problem and is addressed by the Central Limit Theorem. For now‚ let us not bother about what this theorem states but we will look at how it could help us in answering our question. The Central Limit Theorem tells us that if we take very many
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Practice Problems for Confidence Intervals X ± Z σ/n ; X ± t s/n ; p ± Z (p(1-p)/n) 1. A press release issued by our university claims that West Chester students study at least as much as the national average for students at four year universities. Across the nation‚ 73 percent of all students at four year universities study at least four hours per week. Seventy percent of one hundred randomly selected West Chester students surveyed claimed to study more than four hours per week.
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estimate the proportion of X-ray machines that malfunction and produce excess radiation. A random sample of 40 machines is taken and 12 of the machines malfunction. The problem is to compute the 95% confidence interval on π‚ the proportion that malfunction in the population. Solution: The value of p is 12/40 = 0.30. The estimated value of σp is = 0.072. A z table can be used to determine that the z for a 95% confidence interval is 1.96. The limits of the confidence interval are therefore:
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the normal distribution with a standard deviation of $40‚000. a. If we select a random sample of 50 households‚ what is the standard error of the mean? b. What is the expected shape of the distribution of the sample mean? c. What is the likelihood of selecting a sample with a mean of at least $112‚000? d. What is the likelihood of selecting a sample with a mean of more than $100‚000? e. Find the likelihood of selecting a sample with a mean of more than $100‚000 but less than $112‚000. a) The standard
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A Study in Determining Confidence Intervals at 95% Charlesatta Johnson PH6014 October 9‚ 2013 Dr. Rodrick Frazier A Study in Determining Confidence Intervals at 95% As hypothesized‚ high cholesterol levels in children can lead to their children being affected with hyperlipidemia. A study is conducted to estimate the mean cholesterol in children between the ages of 2 - 6 years of age. It also attempted to establish a correlation as to the effect family history has on the onset of the disease
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Confidence Intervals have numerous applications for professional activities. Confidence Intervals have a wide use in defining the outcome of a particular question. The use of confidence levels are used commonly in Health‚ Business‚ Politics and Engineering venues. There are three examples that will be recognized as having real world applications regarding confidence intervals. An Empirical Test of the Black-Scholes (BS) Option pricing model exhibited the use of a confidence interval approach
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Statistics reveal that 95% of children and adults experience lack of confidence‚ self-belief‚ or low self-esteem at some point in their lives. Confidence is a feeling most adolescents have always struggled with and it is impossible to overestimate the lack of it amongst students. It ties in with stress‚ peer pressure‚ and other insecurities most teenagers face on a daily basis. Self-confidence can be altered by various life situations such as one’s school environment‚ home life‚ and individual motivation
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is appearing in various forms. Among those are kinetic‚ gravitational potential‚ elastic potential‚ electric potential‚ thermal‚ chemical‚ etc. Work‚ on the other hand‚ is the change in energy from one form to another by means of an external force. When work is done on an object‚ therefore‚ the object is said to have either gained or lost a certain amount of energy of a particular type. The total work done on a particle by all forces that act on it is equal to the change in its kinetic energy‚ also
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