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43. Small, energy-efficient, Internet-centric, new computers are increasingly gaining popularity (The New York Times, July 20, 2008). Some of the biggest companies are wary of the new breed of computers because their low price could threaten PC makers' already thin profit margins. An analyst comments that the larger companies have a cause for concern since the mean price of these small computers has fallen below $350. She examines six popular brands of these small computers and records their retail prices as: 322 269 373 412 299 389 a. What assumption regarding the distribution of the price of small computers is necessary to test the analyst's claim? b. Specify the null and alternative hypotheses to test the analyst's claim. c. Calculate the value of the test statistic and the p-value. d. At the 5% significance level, what is the conclusion to the test? Should the larger computer companies be concerned?44. A local brewery wishes to ensure that an average of 12 ounces of beer is used to fill each bottle. In order to analyze the accuracy of the bottling process, the bottler takes a random sample of 48 bottles. The sample mean weight and the sample standard deviation of the bottles are 11.80 ounces and 0.8 ounce, respectively. a. State the null and the alternative hypotheses to test if the accuracy of the bottling process is compromised. A: b. Do you need to make any assumption regarding the population for testing? _ A: c. Calculate the value of the test statistic and the p-value. _ A: d. At a = 0.05, what is the conclusion to the test? Make a recommendation to the bottler._ A:45. Based on the average predictions of 47 members of the National Association of Business Economists (NABE), the U.S. gross domestic product (GDP) will expand by 3.2% in 2011 (The Wall Street Journal, May 23, 2010). Suppose the sample standard deviation of their predictions was 1%. At the 5% significance level, test if the mean forecast GDP of all NABE members is greater than 3%.46. In September 2007, U.S. home prices fell at a record pace, and price declines in Los Angeles and Orange counties in California outpaced other major metropolitan areas (Los Angeles Times, November 28, 2007). The report was based on the Standard & Poor's/Case-Shiller index that measures the value of single-family homes based on their sales histories. According to this index, the prices in San Diego dropped by an average of 9.6% from a year earlier. Assume that the survey was based on recent sales of 34 houses in San Diego that also resulted in a standard deviation of 5.2%. Can we conclude that the mean drop of all home prices in Page 344 San Diego is greater than the 7% drop in Los Angeles? Use a 1% level of significance for the analysis. A:47. A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The manufacturer tested 12 of the cars and clocked their performance times. Three of the cars clocked in at 5.8 seconds, 5 cars at 5.9 seconds, 3 cars at 6.0 seconds, and 1 car at 6.1 seconds. At the 5% level of significance, test if the new sports car is meeting its goal to go from 0 to 60 miles per hour in less than 6 seconds. Assume a normal distribution for the analysis._ A:41. A machine that is programmed to package 1.20 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and the standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively. a. Set up the null and the alternative hypotheses to determine if the machine is working improperly-that is, it is either underfilling or overfilling the cereal boxes. b. Calculate the value of the test statistic and the p-value. c. At the 5% level of significance, can you conclude that the machine is working improperly? Explain.40. Consider the following hypotheses: Ho: H 2 100 HA: H