First Part Conduct an investigation considering the following concepts: Parameter estimation Point estimator Sampling error Repeated sampling Sampling distribution Standard error of the mean Law of...

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First Part Conduct an investigation considering the following concepts: Parameter estimation Point estimator Sampling error Repeated sampling Sampling distribution Standard error of the mean Law of large numbers Central limit theorem Confidence interval of the population mean Confidence interval of a proportion of the population Guiding questions to answer in writing: Define sampling distribution and distinguish it from a distribution of raw scores from a population. How can you show that a statistic calculated on a single sample only provides an estimate of one parameter? For an interval or ratio variable, explain what the standard deviation and error measure dispersion and how the two statistics are mathematically related. Explain the law of large numbers. Under what circumstances does a sampling distribution of proportions fit the normal distribution? Explain and illustrate with formulas why the standard error of the means will always be less than the standard deviation of the variable under study. Second Part After studying and reviewing the concepts and practices from Workshop 2, answer all the questions provided about the concepts from Module # 2: Probability and Sampling Distributions. 1. Recent studies indicate that the average 50-year-old woman spends $ 350 annually on personal care products. The distribution of the amounts spent is governed by a normal distribution with a standard deviation of $ 45 per year. A random sample of 40 women is selected. The average amount that the sample spends is $ 335. What is the probability of finding a sample mean equal to or greater than that of the indicated population? 2. The mean age at which men marry in the United States for the first time is governed by the normal distribution with a mean of 24.8 years. The standard deviation of the distribution is 2.5 years. For a random sample of 60 men, what is the probability that the age at which they first married is less than 25.1 years? 3. Company XYZ conducts a survey with a sample of 60 companies to study the customer's healthcare costs. One of the elements that is studied is the annual deductible that employees must pay. The Department of Labor reports that the mean of this distribution is $ 502, with a standard deviation of $ 100. a. Find the standard error of the sample mean of XYZ. b. What is the probability that XYZ finds a sample mean between $ 477 and $ 527? c. Find the probability that the sample mean is between $ 492 and $ 512. d. What is the probability that the sample mean is greater than $ 550? 4. A research company conducted a survey to determine the average amount that smokers spend on cigarettes during a week. The company found that the distribution of amounts they spend per week tended to follow a normal distribution, with a standard deviation of $ 5. A sample of 49 smokers revealed that the median expense is $ 20. a. What is the point estimator of the population mean? Explain what it indicates. b. Using the 95% confidence level, determine the confidence interval of μ. Explain what it means. 5. The US dairy industry wants to calculate average milk consumption per year. A sample of 16 people reveals that the average annual consumption is 60 gallons, with a standard deviation of 20 gallons. a. What is the value of the population mean? What is the best estimator of this value? b. Explain why you need to use the t distribution. What assumptions do you need to make? c. What is the value of t in a 90% confidence interval? d. Construct the 90% confidence interval of the population mean. e. Is it reasonable to conclude that the population mean is 63 gallons? Explain 6. As a requirement to obtain employment, candidates from a company must pass a drug test. Of the last 220 applicants, 14 failed. Build the 99% confidence level of the proportion of applicants who fail the test. Is it reasonable to conclude that more than 10% of applicants do not pass it? Explain Consider the following when submitting your test: • Present your answers with the aspects learned so far about probability and sampling distributions. • Use the APA style manual when submitting your proof in MS Word document.