# Livestock are given a special feed supplement to see

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Chapter 5 / Exercise 1
Research Methods and Statistics: A Critical Thinking Approach
Jackson
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223.Livestock are given a special feed supplement to see if it will promote weight gain. The researchers’ report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of error of ±11 pounds. Some students wrote the following conclusions. Did anyone interpret the interval correctly? Explain any misinterpretations.(a)95% of the cows studied gained between 45 and 67 pounds.(b)We’re 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.(c)We’re 95% sure that the average weight gain among the cows in this study was between 45 and 67 pounds.(d)The average weight gain of cows fed this supplement will be between 45 and 67 pounds 95% of the time.(e)If this supplement is tested on another sample of cows, there is a 95% chance that their average weight gain will be between 45 and 67 pounds.224.In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 40 years. We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year. Do you think the necessary assumptions for inference are satisfied? Explain. The men in our sample married at an average age of 24.2 years with a standard deviation of 5.3 years. What’s the P-value for this result? What’s your conclusion? Use a .05 level of significance.225.Students investigating the packaging of potato chips purchased 6 bags of Lay’s Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in 33
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Chapter 5 / Exercise 1
Research Methods and Statistics: A Critical Thinking Approach
Jackson
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grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5. Create a 95% confidence interval for the mean weight of such bagsof chips. Explain in context what your interval means. Comment on the company’s stated net weight of 28.3 grams.226.One of the important factors in auto safety is the weight of the vehicle. Insurance companies are interested in knowing the average weight of cars currently licensed in the United States; they believe it is 3000 pounds. Tosee if that estimate is correct, they checked a random sample of 91 cars. For that group the mean weight was 2919 pounds, with a standard deviation of 531.5 pounds. Is this strong evidence that the mean weight of all cars is not 3000 pounds? Use a .01 level of significance. 227.A manufacturer claims that a new design for a portable phone has increased the range to 150 feet, allowing many customers to use the phone throughout their homes and yards. An independent testing laboratory foundthat a random sample of 44 of these phones worked over an average distance of 142 feet, with a standard deviation of 12 feet. If there evidence that the manufacturer’s claim is false? Use a .05 level of significance.