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SELECTED ANSWERS Chapter 1: What Is Statistics 1.1 a. The population of interest is the weight of shrimp maintained on the specific diet for a period of 6 months. b. The sample is the 100 shrimp selected from the pond and maintained on the specific diet for a period of 6 months. c. The weight gain of the shrimp over 6 months. d. Since the sample is only a small proportion of the whole population, it is necessary to evaluate what the mean weight may be for any other randomly selected 100 shrimps. 1.5 a. All football helmets produced by the five companies over a given period of time. b. The 540 helmets selected from the output of the five companies. c. The amount of shock transmitted to the neck when the helmet’s face mask is twisted. d. The neck strength of players is extremely variable for high school players. Hence, the amount of damage to the neck varies considerably from player to player for exactly the same amount of shock transmitted by the helmet. Chapter 2: Using Surveys and Scientific Studies to Gather Data 2.1 The relative merits of the different types of sampling units depends on the availability of a sampling frame for individuals, the desired precision of the estimates from the sample to the population, and the budgetary and time constraints of the project. 2.3 A more precise estimate can be obtained by considering individual cars but it may be very difficult obtaining the sampling frame. By selecting parking lots and examining all cars in the lot, the data is more easily obtained but the individual cars in the lot may have common characteristics reflecting the set of persons using the parking lot. Thus, the cars in the lot are a cluster sample and not a simple random sample. This results in a less precise estimate of the population than examining the same number of cars selected individually. 1

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2.5 The agency could stratified farms based on the total acreage of farms in the state. A simple random sample of farms could then be selected within each strata and a questionaire sent to the farmer. 2.9 a. No. The survey in which the interviewer showed the peanut butter should be the more accurate because it does not rely on the respondent’s memory of which brand was purchased. b. Both surveys may have survey nonresponse bias because an entire segment of the population (those not at home) cannot be contacted. Also, both surveys may have interviewer bias resulting from the way the question is posed (e.g., tone of voice). In the first survey, results may be biased by the respondent’s ability to recall correctly which brand was purchased. The second survey may be biased by the respondent’s unwillingness to show the interviewer the peanut butter jar (too intrusive), or by the respondent not recognizing that the peanut butter that had purchased was low fat .
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