Chapter 08, Section 8.2, Intelligent Tutoring Problem 011 For a data set obtained from a sample of size n = 81 with x = 50.25, it is known that o = 4.1. (a) What is the point estimate of p? (b) Find z score corresponding to a 95% confidence level, z/2. Recall that (1 - a)100% = 95%. (c) Construct a 95% confidence interval for p. (d) What is the margin of error in part (c)? Recall the following definitions from section 8.2-3 of the text. The confidence level is denoted by (1 - a)100%, where a is called the significance level. a = P(|Z| > z). By symmetry, a/2 = P(Z > z). The endpoints for a (1 - a)100%, confidence interval for u, if o is known and either the population is normal or n 2 30, are given by I+ zoz where the value of z is obtained from the standard normal distribution (Table IV in Appendix C or by calculator) and oz = is the standard deviation of I. Vn The quantity zoz is called the Margin of Error and is denoted by E. To obtain z from a graphing calculator we use the formula z = invNorm(1 - a/2, p, o) where p is the mean and o is the standard deviation of the normal distribution. For standard normal distribution p = 0 and o = 1. Recall that in general z = invNorm("area to left of z", p, o) Chapter 08, Section 8.2, Intelligent Tutoring Problem 011 For a data set obtained from a sample, n = 81 and x = 50.25. It is known that o = 4.1. (a) What is the point estimate of u? (b) Find a corresponding to a 95% confidence level. (c) Find 1 - 0a/2. 1 - a/2 = (d) Find to 2 decimal places Za/2 for 95% confidence level. Za/2 =

Suppose a new treatment for a certain disease is given to a sample of 180 patients. The treatment was successful for 153of the patients. Assume that these patients are representative of the population of individuals who have this disease. Calculate a 98% confidence interval for the proportion successfully treated. (Round the answers to three decimal places.)

Suppose you are planning an experiment and a sample has yet been selected. For this experiment you plan on taking a SRS of 50 mice with pancreatic cancer measuring a particular hormone level. What would be the impact on a 95% confidence interval calculated from the experiment on these mice if instead of a SRS of 50 mice, a SRS of 200 mice were taken?

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 2.12

Suppose that you are interested in the number of people in each household in the U.S. Your sample includes 10 households, with a mean 2.5 and a standard deviation 1.2. Construct a 95% confidence interval (CI) of the mean number of household members.  (A) 1.2-3.8 (B) 1.4-3.6 (C)1.6-3.4 (D) 1.7-3.3 (E) 1.8-3.2

A sample of size n=77 is drawn from a population whose standard deviation is 0= 33. Part 1 of 2 (a) Find the margin of error for a 95% confidence interval for µ. Round the answer to at least three decimal places. The margin of error for a 95% confidence interval for µ is Part 2 of 2 (b) If the confidence level were 90%, would the margin of error be larger or smaller? (Choose one) ▼ because the confidence level is (Choose one) ▼

A sample of size n=89 is drawn from a population whose standard deviation is a 16. Part 1 of 2 (a) Find the margin of error for a 90% confidence interval for μ. Round the answer to at least three decimal places. The margin of error for a 90% confidence interval for μ is. Part 2 of 2 (b) If the sample size were n=87, would the margin of error be larger or smaller? (Choose one) , because the sample size is (Choose one)

From chapter 14, review activity #19. A recent survey of 200 households showed that 8 had a single male as the head of the household. Forty years ago, a survey of 200 households showed that 6 had a single male as the head of the household. Car it be concluded that the proportion has changed, based on a 95% confidence interval? Recall the confidence interval is calculated as (-0.0261, 0.0461) A) Yes, the proportion changed since 0 is in the interval. B) Yes, the proportion changed since O is NOT in the interval. C) No, the proportion did not change since 0 is in the interval. D) No, the proportion did not change since 0 is NOT in the interval. E) We cannot determine the conclusion from the confidence interval

According to a Field Poll, 263 out of 569 of California adults feel that "education and our schools" is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education and the schools is one of the top issues facing California. The error bound is ___________  rounded to 4 decimal places.