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Chapter Problems Problem 1 The manufacturer of the new subcompact Clipper claims in their TV advertisements that it will average “6.25 litres per 100 km or less on the open road.” Some of the competitors believe this claim is exaggerated. To investigate, an independent testing agency is hired to conduct tests. A random sample of 36 Clippers showed their mean litres per 100 km to be 6.8 with a sample standard deviation of 1.5 litres per 100 km. At the 0.01 significance level can the manufacturer's claim be refuted? Determine the p value. Interpret the result. Exercise 9.1 Check your answers against those in the ANSWER section. Last year the records of Dairy Land Inc., a convenience store chain, showed the mean amount spent by a customer was $30. A sample of 40 transactions this month revealed the mean amount spent was $33 with a standard deviation of $12. At the 0.05 significance level, can we conclude that the mean amount spent has increased? What is the p-value? Follow the five-step hypothesis testing procedure. Problem 2 The mean construction time for a standard two-car garage by Arrowhead Construction Company is 3.5 days. The time for the construction process follows the normal distribution. The construction process is modified through the use of a “quick setting concrete” for the foundation and floor. This should allow the next phase of construction to start in a more timely manner. A sample of 12 garages had a mean construction time of 3.0 days with a standard deviation of 0.9 days. Does use of the quick setting concrete decrease the construction time? Exercise 9.2 Check your answers against those in the ANSWER section. The mean construction time for a standard two-car garage by Arrowhead Construction Company is 3.5 days. The time for the construction process follows the normal distribution. The construction process is modified through the use of “precut and assembled roof trusses” rather than onsite construction of roof rafters. This should shorten the construction time. A sample of 15 garages had a mean time of 3.40 days with a standard deviation of 0.8 days. Does use of the “precut and assembled roof trusses” decrease the construction time? Follow the five-step hypothesis testing procedure using the 0.05 significance level. Problem 3 The Bunting Brass & Bronze Company has a computer controlled machine that is programmed to do precision cutting of a circular brass disc with a mean diameter of 6.125 centimetres. The shop foreman takes a random sample of 8 discs from the production line. The diameters are as follows: 6.115 6.127 6.129 6.113 6.124 6.121 6.131 6.124 The foreman suspects that the machine is out of adjustment. Use the hypothesis testing procedure to determine if the programmer needs to make adjustments. 153 Chapter 9 One-Sample Tests of A Hypothesis Exercise 9.3 Check your answers against those in the ANSWER section. A typical college student spends an average of 2.55 hours a day using a computer. A sample of 13 students at Findlay College revealed the following number of hours per day using the computer: 3.15 3.25 2.00 2.50 2.65 2.75 2.35 2.85 2.95 2.45 1.95 2.35 3.75 Can we conclude that the mean number of hours per day using the computer by students at Findlay College is the same as the typical students usage? Use the hypothesis testing procedure and the 0.05 significance level. Problem 4 The Dean of Students at Scandia Tech believes that 30 percent of the students are employed. You, as President of the Student Government, believe the proportion employed is less than 30 percent and decide to conduct a study. A random sample of 100 students revealed 25 were employed. At the 0.01 significance level, can the Dean's claim be refuted? Exercise 9.4 Check your answers against those in the ANSWER section. The producer of a TV special expected about 40 percent of the viewing audience to watch a rerun of a 1965 Beatles Concert. A sample of 200 homes revealed 60 to be watching the concert. At the 0.10 significance level, does the evidence suggest that less than 40 percent were watching? Use the usual hypothesis testing format. What is the p-value? 154 Chapter 9 One-Sample Tests of A Hypothesis