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A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 31 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was 52.1. Another random sample of 21 trucks were fitted with the old fuel injection system and driven under a variety of different conditions. For these trucks, the sample variance of gasoline consumption was 31.6. Test the claim that there is a difference in population variance of gasoline consumption for the two injection systems. Use a 5% level of significance. How could your test conclusion relate to the question regarding the consistency of fuel consumption for the two fuel injection systems?
What are the degrees of freedom?
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- A snow shovel manufacturer is considering a new shovel with small holes punched in it, thought to reduce energy expenditure of the user. The data in the Problem 4 tab provides information for 13 workers using both the conventional shovel and the perforated shovel. Does the data suggest that the energy expenditure of the perforated shovel is lower than that of the conventional shovel? Does the data suggest that the variance of the two shovels is different?arrow_forwardAn agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 20 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 20 differences (Variety A - Variety B) givex¯=3.2x¯=3.2 and s=4.63s=4.63. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (Type "mu" for the symbol μμ , e.g. mu >> 1 for the mean is greater than 1, mu << 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1) H0H0 : HaHa : (b) Find the test statistic, t = (c) Answer the question: Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance) (Type: Yes or No)arrow_forwardBusinesses know that customers often respond to background music. Do they also respond to odors? One study of this question took place in a small pizza restaurant in France on two Saturday evenings in May. On one of these evenings, a relaxing lavender odor was spread through the restaurant. On the other evening no scent was used. The data gives the time, in minutes, that two samples of 30 customers spent in the restaurant and the amount they spent in euros. No odor Lavender Minutes Euros spent Minutes Euros spent 103103 15.915.9 9292 21.921.9 6868 18.518.5 126126 18.518.5 7979 15.915.9 114114 22.322.3 106106 18.518.5 106106 21.921.9 7272 18.518.5 8989 18.518.5 121121 21.921.9 137137 24.924.9 9292 15.915.9 9393 18.518.5 8484 15.915.9 7676 22.522.5 7272 15.915.9 9898 21.521.5 9292 15.915.9 108108 21.921.9 8585 15.915.9 124124 21.521.5 6969 18.518.5 105105 18.518.5 7373 18.518.5 129129 25.525.5 8787 18.518.5 103103 18.518.5 109109 20.520.5 107107…arrow_forward
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- The medical researcher is comparing two treatments for lowering cholesterol: diet and meds. The researcher wants to see if the patients who receive the recommendation to change their diet have less success lowering cholesterol compared to a prescription of meds. A random sample of some patients who received the recommendation to change their diet and others who were prescribed meds was taken. The results of how many did or did not lower their cholesterol are shown below: Data on Diet vs. Meds for Weight Los Diet Meds Yes 416 483 No 266 248 What can be concluded at the a = 0.05 level of significance? %3D For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer > Select an answer Select an answer O (please enter a decimal) Hj: Select an answer Select an answer Select an answer O (Please enter a decimal) b. The test statistic ? O (please show your answer to 3 decimal places.) c. The p-value = (Please show your answer to %3D 4…arrow_forwardA test is being designed to compare the wearing quality of two brands of tires, say brand A and brand B. Six automobiles will be selected and equipped with the new tires from both brands and driven under normal conditions for 1 month. A measurement will be taken to determine how much wear took place on a scale from 0 to 200. Below is a table of the paired data collected from the 6 cars in the test. [BrandA BrandB] 125 64 64 65 94 103 38 37 90 102 106 115 Conduct a hypothesis test to determine whether the mean of the difference population is 0 at a significance level of a =. State your conclusion.arrow_forwardIn college, talented runners may join a cross-country team. Runners tend to run their best times when they run even splits. Even splits occur when the runners maintain an even pace throughout the race. The cross-country coach wants to estimate the typical variability in his best runner's 1-mile splits. He takes a random sample of 25 of this runner's mile splits and finds that this runner's mean 1-mile split is 5.44 minutes per mile, with a standard deviation of 0.14 minutes per mile. This runner's 1-mile splits follow a normal distribution. (a) Find the chi-square critical values XL² and Xu² to be used in constructing a 95% confidence interval for the true population standard deviation. (Round your answers to two decimal places.) XL²= XU²= (b) Find the 95% confidence interval for the true variability in his best runner's 1-mile splits. (Round your answers to three decimal places.) lower bound and the upper boundarrow_forward
- What percentage of Contra Costa County adults supports a ban on assault-style weapons? Suppose that we survey a random sample of 100 adults living in Contra Costa County and find that 62% support a ban on assault-style weapons. According to a 2015 study by the Pew Research Center, 57% of U.S. adults favor a ban on assault-style weapons. Assuming that the variability in random samples will be the same in Contra Costa County as in the U.S., find the 95% confidence interval to estimate the proportion of CCC adults that favor a ban on assault-style weapons. g. Are we confident that the percentage of Contra Costa County residents that supports a ban is greater than the percentage nationwide as reported by the Pew Research Center? Why or why not?arrow_forwardPETROGAS is testing new filters for its motorbikes. One brand of filter (Filter A) is placed in one motorbike, and the other brand (Filter B) is placed in the second motorbike. Random samples of air released from the motorbikes are taken at different times throughout the day. Pollutant concentrations are measured for both motorbikes at the same time. The following data attached represent the pollutant concentrations (in parts per million) for samples taken at 20 different times after passing through the filters. a. Test the hypothesis that the mean for the pollutant concentration for Filter B is greater than 30. Use the 1% level of significance. b. Construct a 95% confidence interval for the difference in mean pollutant concentration, where a difference is equal to the pollutant concentration passing through Filter A minus the passing through Filter B. c. Using the 5% significance level, determine whether there is evidence that mean for the pollutant concentration for Filter A…arrow_forwardAn athletic director proudly states that he has used the average GPAs of the university's sports teams and is predicting a high graduation rate for the teams. Why is this method unsafe? Choose the correct answer below. OA. This method is unsafe because the average GPA may differ for each team. Using the average of the average GPA of each team obscures the possibility that certain teams tend to perform less well in classes. B. This method is unsafe because there is more variation in the GPAs of the athletes than the average GPA of the university's sports teams. Strong students may offset weak students in calculating the average GPAS, which makes it appear more likely that most students are doing well. OC. This method is unsafe because it is dangerous to extrapolate into the future. Classes in university tend to become more difficult, which makes it less likely that the average GPA will hold as time goes on. D. This method is unsafe because there is a minimum GPA required to graduate. If…arrow_forward
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