(2) Maximum likelihood estimators are unbiased.
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- A marketing representative wants to estimate the proportion of people in a state who like the new design on the packaging of a certain cleaning product. The representative interviewed 100 people at a certain supermarket, and 82 people indicated that they liked the new design. Have the conditions for creating a confidence interval for the population proportion been met? Yes, because the sample was selected at random. A Yes, because sampling distributions of population proportions are modeled with a normal model. B Yes, because the sample is large enough to satisfy the normality conditions. C No, because the sample is not large enough to satisfy the normality conditions. D No, because the sample may not be representative of all people in the state.(a) A study is interested in the proportion of postgraduate students who have met the criteria of depression during their study periods. In a random sample of 50 postgraduate students, 15 are found to be afflicted. Use the normal distribution table to construct a 98% confidence interval for the proportion of postgraduate students who have experienced depression. What can we assert with 98% confidence about the possible size of our error if we estimate the proportion to be 0.30?G The Ball Corporation's beverage X 17-2 Homework Chapter 8 (Sectic X ezto.mheducation.com/ext/map/index.html?_con=con&external_browser=0&launchUrl=https%253A%252F%252Fnewconnect.mheducation.com... A k: Chapter 8 (Sections 8.1 and 8.5) The 98% confidence interval is from a to The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation 0.000965 mm. Assume a random sample of 58 sheets of metal resulted in an = .3193 mm. Calculate the 98 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.) Help 4 Save & Exit Check m
- You are given the following information about a random sample: (i) The sample size is 5. (ii) The sample is from a Weibull distribution with t = 2. (iii) Two of the sample observations are known to exceed 50, and the remaining three observa- tions are 20, 30 and 45. Calculate the maximum likelihood estimate of 0. (a) 32.678 (b) 42.678 (c) 52.678 (d) 62.678 (e) 72.678need help with followingA clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 520 babies were born, and 286of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective? ________________________<p<______________________ does the method appear to be effective?
- Which of the following is often true for very large samples Significance tests are likely to produce statistically significant results even when the true value is close to the null value. The results will be statistically significant only when there is a true difference between the parameter and the null value. Significance tests are likely to produce nonsignificant results when the true value is close to the null value. A confidence interval will likely cover all possible values in the population.Suppose that the proportion of investors who are risk-averse (that is, try to avoid risk in their investment decisions) is though to be at least 0.7. A financial advisor believes that the proportion is actually less than 0.7. A survey of 35 investors found that 23 of them were risk-averse. Formulate a one-sample hypothesis test for a proportion to test this belief. Determine the null hypothesis, H,, and the alternative hypothesis, H,. Ho H,: (Type integers or decimals. Do not round.) Compute the test statistic. (Round to two decimal places as needed.) Find the p-value for the test. (Round to three decimal places as needed.) State the conclusion at the 0.05 level of significance. The p-value is V the chosen value of a, so the null hypothesis. There is evidence to conclude that the proportion of investors who are risk-averse is not at least 0.7.A sample of 10 observations taken from a normally distributed population yielded the following data.46 54 30 48 46 39 47 36 41 56
- Suppose we take the Bayesian viewpoint. We want to understand the probability of someone responding positively to a vaccine. Our parameter of interest is p the probability of a positive reaction. We specify our prior belief on p using a Beta distribution with parameters (shape 1 and shape 2) given by 4 and 8. We take 100 people (assumed to be a random sample), administer the vaccine, and see how many successes we have. We can reasonably model our data using a Binomial distribution with parameters 100 and p. Our updated belief follows a new Beta distribution with parameters (shape 1 and shape 2) given by 44 and 68. What is the posterior mean? Report your answer to three decimal places. What is the lower bound of an equal tail 95% credible interval for p? That is, report the 0.025 quantile of the posterior distribution.You may need to use the appropriate appendix table or technology to answer this question. Recall the method used to obtain a confidence interval for the difference between two population means for matched samples. (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 - Population 2.) Population Element 1 Difference 1 11 8 7 8 3 9 6 4 12 13 10 6 15 15 15 14 (b) Compute d. (c) Compute the standard deviation s. (Round your answer to two decimal places.) (d) What is the point estimate of the difference between the two population means? (Use Population 1 - Population 2.) (e) Provide a 95% confidence interval for the difference between the two population means. (Use Population 1 - Population 2. Round your answers to two decimal places.) to11. What does the least squares method do exactly? a. Minimizes the errors between the actual model values and the estimated model values. b. Maximizes the distance between the parameters and the estimators. c. Finds the best regression model. d. Minimizes the distance between the parameters and the estimators. e. All the above. 12. Which of the following is an assumption of T-test for testing several populations? a. All the random variables within the k populations follow a normal distributions. b. The samples associated with each population are randomly selected and are independent from all other samples. c. The variances of all random variables should be homogenous. d. The correlation coefficient between the random variablescshould be significant. e. All of the above 13. In a one-way ANOVA, which of the following statements is correct? There are multiple interactions. b. The error sum square is moderately small in one-way ANOVA The interaction can increased the efficiency of one-way…