3. When automobile companies advertise the gasoline consumption of a particular model, they give the average miles per gallon for that model. Standards require that the estimate must be within plus or minus 1¼ miles of the true average, with a 95% confidence level. A new model called the Shark is being marketed, and the advertising director needs to know what average miles per gallon to use in the advertisements. Prototype testing indicates the Shark typically gets between 13 and 29 miles per gallon, depending upon the type of driving conditions. How large of a sample of Sharks must be tested in order to obtain the average miles per gallon to be used in the advertisements?
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- The National Weight Control Registry tries to mine secrets of success from people who lost at least 30 pounds and kept it off for at least a year. It reports that out of 2,720 registrants, 439 were on a low-carbohydrate diet (less than 90 grams a day). a. Develop a 95% confidence interval for the proportion of people on a low-carbohydrate diet.b. Is it possible that the population percentage is 16%? c. How large a sample is needed to estimate the proportion within 0.55%?After reporting the results from a formal hypothesis test, it is often likely that statisticians will report a confidence interval in order to indicate that a null value is present, indicating a significant response . True FalseA 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain areawho favor moving the broadcast of the late weeknight news to an hour earlier than it is currently. Initially, theconfidence interval will be created using a simple random sample of 9,000 viewers in the area. Assuming that thesample proportion does not change, what would be the relationship between the width of the original confidenceinterval and the width of a second 90 percent confidence interval that is created based on a sample of only 1,000viewers in the area?(A) The second confidence interval would be 9 times as wide as the original confidence interval.(B) The second confidence interval would be 3 times as wide as the original confidence interval.(C) The width of the second confidence interval would be equal to the width of the original confidence interval.(D) The second confidence interval would be 1/3 as wide as the original confidence interval.(E) The second…
- On the basis of the results to part A in the picture, does the manager have a right to complain to the manufacturer?  does a 1 gallon paint can containing exactly 1 gallon of paint lie within the 95% confidence interval? A recent survey of cell phone users indicated that 56 percent of the respondents prefer to use cell phones for texting rather than for making phone calls. A 95 percent confidence interval for the estimate of all cell phone users who prefer to use cell phones for texting has a margin of error of 3 percent. Assume all conditions for inference have been met. Based on the confidence interval, which of the following claims is supported? Select A, B, C, or D Less than half of all people prefer texting. A More than half of all people prefer texting. B At least 60 percent of all people prefer texting. C At least 75 percent of all people prefer texting. D At least 95 percent of all people prefer texting. EA researcher computed a 90% confidence interval for the proportion of students who smoke. If the researcher had instead used a 95% confidence interval, then the computed margin of error would have been smaller. True False
- The production manager in an automobile plant is concerned with the number of cars that do not pass the final quality control inspection. In the last two hours he noted that in a sample of 120 cars only 92 were acceptable. The lower and upper limit of a 95% confidence interval for the true percentage of all cars that would not pass the final quality control inspection would be:A research group studying cell phone habits asked the question “Do you ever use your cell phone to make a payment at a convenience store?” to people selected from two random samples of cell phone users. One sample consisted of older adults, ages 35 years and older, and the other sample consisted of younger adults, ages 18 years to 34 years. The proportion of people who answered yes in each sample was used to create a 95 percent confidence interval of (0.097,0.125)(0.097,0.125) to estimate the difference (younger minus older) between the population proportions of people who would answer yes to the question. Which of the following is the best description of what is meant by 95 percent confidence? In repeated random sampling with the same sample size, approximately 95% of the sample proportions from the younger group will be between 0.097 and 0.125 greater than the sample proportion from the older group. A In repeated random sampling with the same sample size,…What effect would increasing sample size have on a confidence interval? What effect would decreasing sample size have on the margin of error?
- If we want both intervals to hold at the 90% level of confidence, then the individual intervals must hold at a higher level of confidence. Write a brief but detailed explanation of how this could be of importance in a large, complex engineering design such as a rocket booster or a spacecraft.A researcher surveys 50 individuals in Smithville and 40 in Amherst, finding that 30% of smithville residents moved last year, while only 22% of Amherst residents did. Is there enough evidence to conclude that mobility rates in the two communities differ? Use a two-tailored alternative, and a=0.10. Again, find the p-value and a 90% confidence interval for the difference in proportionsAn epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 339 people living in East Vancouver and finds that 40 have recently had the flu. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of East Vancouver residents who have recently had the flu. A. 11.80% (40/339) of East Vancouver residents have recently had the flu. ? true false B. There is a 95% probability that the true proportion of East Vancouver residents who have recently had the flu equals 40/339. ? true false C. If another random sample of 339 East Vancouver residents is drawn, there is a 95% probability that the sample proportion of East Vancouver residents who have recently had the flu equals 40/339. ?…