What is a confidence-interval estimate of a parameter? Why is such an estimate superior to a point estimate?
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- A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Using this data, find the 90%90% confidence interval for the true difference in blood pressure for each patient after taking the new drug. Assume that the blood pressures are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 195195 167167 197197 187187 187187 186186 204204 178178 172172 Blood pressure (after) 181181 158158 174174 172172 162162 162162 185185 167167 146146 Copy Data Step 4 of 4 : Construct the 90%90% confidence interval. Round your answers to one decimal place.(g) Suppose a new movie (based on an epic novel) has just been released. Production costs were x2 = 11.4 million; promotion costs were x3 = 4.7 million; book sales were x4 = 8.1 million. Make a prediction for x1 = first-year box office receipts and find an 85% confidence interval for your prediction (if your software supports prediction intervals). (Use 1 decimal place.) prediction lower limit upper limit (h) Construct a new regression model with x3 as the response variable and x1, x2, and x4 as explanatory variables. (Use 2 decimal places.) x3 = + x1 + x2 + x4 Suppose Hollywood is planning a new epic movie with projected box office sales x1 = 100 million and production costs x2 = 12 million. The book on which the movie is based had sales of x4 = 9.2 million. Forecast the dollar amount (in millions) that should be budgeted for promotion costs x3 and find an 80% confidence interval for your prediction. prediction lower limit upper limitA pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Using this data, find the 90%90% confidence interval for the true difference in blood pressure for each patient after taking the new drug. Assume that the blood pressures are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 174174 176176 204204 180180 204204 189189 177177 181181 187187 Blood pressure (after) 166166 164164 194194 157157 178178 178178 156156 175175 178178 Step 2 of 4 : Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.
- I can’t figure out how to solve for the confidence level, I’m not sure if I’m plugging in the wrong numbers or missing a stepExplain the difference between a point estimate of a parameter and a confidence-interval estimate of a parameter.A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Using this data, find the 99%99% confidence interval for the true difference in blood pressure for each patient after taking the new drug. Assume that the blood pressures are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 189189 185185 180180 202202 171171 176176 158158 164164 199199 Blood pressure (after) 178178 176176 168168 196196 153153 156156 147147 144144 188188 Copy Data Step 1 of 4 : Find the point estimate for the population mean of the paired differences. Let x1x1 be the blood pressure before taking the new drug and x2x2 be the blood pressure after taking the new drug and use the formula d=x2−x1d=x2−x1 to calculate the…
- The data below were collected in a clinical trial to compare a new drug to a placebo for its effectiveness in lowering total serum cholesterol. Generate a 95% confidence interval for the difference in mean total cholesterol levels between treatments. Generate a 95% confidence interval for the proportion of all patients with total cholesterol < 200. New Drug Placebo Total Sample (n=75) (n=75) (n=150) Mean (SD) Total Serum Cholesterol 185.0 (24.5) 204.3 (21.8) 194.7 (23.2) % Patients with Total Cholesterol < 200 78.00% 65.00% 71.50% a. 95% CI ( , )In a large scale study of energy conservation in single family homes, 20 homes were randomly selected from homes built in a housing development in southern England. Ten of the houses, randomly selected from the 20 houses selected for the study, were constructed with standard levels of insulation (70 mm of roof insulation and 50 mm of insulation in the walls). The other 10 houses were constructed with extra insulation (120 mm of roof insulation and 100 mm of insulation in the walls). Each house was heated with a gas furnace and energy consumption was monitored for eight years. The data shown below give annual gas consumption in MWh for each of the 20 houses. Standard Insulation Extra Insulation 13.8 15.1 17.8 13.9 18.0 15.9 17.3 17.2 16.9 15.2 19.9 13.8 13.6 11.3 17.6 13.2 15.9 18.8 12.3 14.0 Sample means Sample Standard Deviation 16.31 14.84 2.38 2.12The national average for the percentage of high school graduates taking the SAT is 49%, but the state averages vary from a low of 4% to a high of 92%. A random sample of 317 graduating high school seniors was polled across a particular tristate area, and it was found that 171 had taken the SAT. Estimate the lower boundary of the true proportion of high school graduates in this region who take the SAT with 95% confidence. Only the final answer should be rounded-off to THREE decimal places.
- Suppose that administrators at a large urban high school want to gain a better understanding of the prevalence of bullying within their school. They select a random sample of 280 students who are asked to complete a survey anonymously. Of these students, 91 report that they have experienced bullying. Use this information to find a 95% z-confidence interval for p, the true proportion of students at this school who have experienced bullying. Give the limits (bounds) of the confidence interval as a proportion, precise to three decimal places. lower limit = upper limit =What is the 90% confidence interval for the slope of square footage?Help me answer the last one. A random sample of home runs hit by Major League baseball players was selected, and their exit velocities were recorded below. Assuming that home run exit velocities are close to normally distributed, construct a 95% confidence interval for the mean exit velocity of a home run hit by a Major League baseball player.Exit Velocities (mph) 103 100.6 99.1 98.1 98.8 101.9 103.3 106 114.1 115.2 112.7 103.5 114.3 110.3 115.8 110.1 Choose one: Since we know the population standard deviation, we should use the t-statistic. Since we only know the sample standard deviation, we should use the t-statistic. Since we only know the sample standard deviation, we should use the z-statistic. Since we know the population standard deviation, we should use the z-statistic. Correct Does the given information satisfy the normality requirement? Yes; baseballs are made of leather, which is totally normal. No; we must have a sample size of at least 30. No; we must…
