Download Discussion Worksheet on Confidence Intervals - Introduction to Statistics I | STAT 1000 and more Assignments Statistics in PDF only on Docsity! 1 STAT 1000 Discussion Worksheet – Confidence Intervals Name ____________________ These are some examples of confidence interval problems. 1] Losing weight. A Gallup Poll in November 2002 found that 51% of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of sampling error is ± 3 percentage points.” a) What is the 95% confidence interval for the percent of all adults who want to lose weight? b) What does it mean to say that we have “95% confidence” in this interval? 2] Explaining confidence. A student reads that a 95% confidence interval for the mean NAEP quantitative score for men of ages 21 to 25 is 267.8 to 276.2. Asked to explain the meaning of this interval, the student says, “95% of all young men have scores between 267.8 and 276.2.” Is the student right? Justify your answer. 3] More on NAEP test scores. Suppose that you give the NAEP test to an SRS of 1000 people from a large population in which the scores have mean 280 and standard deviation σ = 60. The mean x of the 1000 scores will vary if you take repeated samples. a) The sampling distribution of x is approximately Normal. It has mean 280=µ . What is its standard deviation? b) Sketch the Normal curve that describes how x varies in many samples from this population. Mark the mean 280=µ and the values, one, two, and three standard deviations on either side of the mean. 2 5] The tale of the scale. A laboratory scale is known to have a standard deviation of 001.0=σ grams in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. Three weighings of a specimen give (in grams) 3.412 3.414 3.415 Give a 95% confidence interval for the true weight of the specimen. What are the estimate and the margin of error in this interval? 6] IQ test scores. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: 114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93 a) We expect the distribution of IQ scores to be close to Normal. Make a stemplot of the distribution of these 31 scores (split the stems) to verify that there are no major departures from Normality. The stemplot is: b) Treat the 31 girls as an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be 15=σ . Give a 99% confidence interval for the mean score in the population.
