378 Chapter 8 Confidence Intervals a standard deviation �� = 8. A single measurement of the concentration is made, and its value is 85. a. Use the methods of Section 8.1 to construct a 95% confidence interval for the mean concentration. (69.3, 100.7) b. Would it be possible to construct a confidence interval using the methods of this section if the population standard deviation were unknown? Explain. No Answers to Check Your Understanding Exercises for Section 8.2 1. a. 2.145 b. 2.831 c. 1.671 d. 12.706 2. a. Yes b. No c. Yes d. No 3. 8.03 < �� < 8.21 4. 744.2 < �� < 756.2 5. a. 14 b. 2.977 c. 40.30 < �� < 50.82 6. a. 9 b. 3.250 c. 8.4811 < �� < 8.7115 SECTION 8.3 Confidence Intervals for a Population Proportion Objectives 1. Construct a confidence interval for a population proportion 2. Find the sample size necessary to obtain a confidence interval of a given width 3. Describe a method for constructing confidence intervals with small samples Objective 1 Construct a confidence interval for a population proportion Construct a Confidence Interval for a Population Proportion Are you a Guitar Hero? The music organization Little Kids Rock surveyed 517 music teachers, and 403 of them said that video games like Guitar Hero and Rock Band, in which players try to play music in time with a video image, have a positive effect on music education. Assuming these teachers to be a random sample of U.S. music teachers, we would like to construct a confidence interval for the proportion of music teachers who believe that music video games have a positive effect on music classrooms. This is an example of a population whose items fall into two categories. In this example, the categories are those teachers who believe that video games have a positive effect, and those who do not. We are interested in the population proportion of those who believe there is a positive effect. We will use the following notation. NOTATION ∙ p is the population proportion of individuals who are in a specified category. ∙ x is the number of individuals in the sample who are in the specified category. ∙ n is the sample size. ∙ ̂p is the sample proportion of individuals who are in the specified category. ̂p = x∕n To construct a confidence interval, we need a point estimate and a margin of error. The point estimate we use for the population proportion p is the sample proportion ̂p = x Explain It Again n The population proportion and the sample proportion: The population proportion p is unknown. The sample proportion p̂ is known, and we use the value of p̂ to estimate the unknown value p. To compute the margin of error, we multiply the standard error of the point estimate by the critical value. The standard error and the critical value are determined by the sampling distribution of ̂p. In Section 7.4 we found that when the sample size n is large enough, the sample proportion ̂p is approximately normal with standard deviation √ p(1 − p) n
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above