Econ 156 Statistics Test 3 Estimation

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Montclair State University *

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ECON 207

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Economics

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Feb 20, 2024

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Econ 156 Test 3 Estimation Using a Single Sample Name ___________________________ 1. Briefly define the following terms in your own words: a) Confidence interval b) The confidence level associated with a confidence interval 2. Under what conditions is the z confidence interval an appropriate way to estimate a population mean? 3. Suppose that a newspaper conducts a survey of a random sample of 120 registered voters in order to predict the winner of a local election. The Republican candidate was favored by 62 of the respondents. a) Construct and interpret a 99% CI for the true proportion of voters who prefer the Republican candidate. b) If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument. 4. Reading comprehension is arguably the single most important skill a student possesses. To assess the current levels of reading comprehension in 3rd grade, 25 students were randomly selected from school district class lists and given a reading comprehension test. The distribution of their scores was approximately normal with a mean of 180 and a standard deviation of 20.12. Construct a 99% confidence interval for the population mean.

5. In a very large school district student records have been kept in three distinct data bases, one each for elementary, middle, and high school. Because of this, data entry errors tend to be compounded as students move through the grades. The district now has a new data base and wishes to fix the original data entry errors. To allocate enough secretarial time to this task, an estimate of the proportion of records that contain errors must be made. Initial estimates are that there are fixable errors in about 15% of the records. Based on the 15% assumption, compute the sample size required to estimate the true proportion of records with errors to within .025 with 95% confidence. 6. Many national parks, wildlife refuges, and wilderness areas lie directly below designated military air space. This raises issues of whether wildlife and, for example, loud jet noises are compatible. In an effort to evaluate the effects of low-altitude jet noise, researchers simulated these noises for captive desert mule deer. Three minutes after the loud noises were played, the heart rates (beats per minute) of these animals was measured, with the following results: 55.9, 51.1, 57.5, 65.5, 68.4, 64.9, 63.1, 55.3, 63.3 Assume that it is reasonable to think that these deer can be regarded as a random sample of desert mule deer. a) Calculate and interpret a 95% confidence interval for the mean heart rate 3 minutes after loud jet noises. b) The mean heart rate for desert mule deer is about 51.2 beats per minute. Based on the confidence interval in part (a), do you think that the loud jet noise has some lingering effect on the heart rate of desert mule deer? Explain 7. Under what conditions is it reasonable to use the t confidence interval to estimate a population mean?

8. The foraging capability of Downy Woodpeckers can be compromised if part of their habitat disappears due to significant human encroachment. These creatures eat insects in trees, and if they cannot find enough food due to a decreasing forest area their body mass may decrease. A 20-year-old study of Downy Woodpeckers indicates that for male Downy Woodpeckers the average mass is about 28g, with a standard deviation of approximately 1.5g. Suppose it is desired to estimate , the average mass of male Downy Woodpeckers in a local forest preserve. If the 20-year old values are taken as reasonable estimates, determine the sample size necessary to estimate meam to within 0.2 grams with 95% confidence.

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