A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. Is the store justified in stating that the average weight of the bags of grapes is 16 ounces?
A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). A doctor commented that, on average, the patients at this clinic have high blood pressure, which is defined as blood pressure over 130. Based on the confidence interval, is the doctor’s statement justified?
A random sample of Roosevelt High School students was asked if they prefer taking notes on a computer or using a paper and pencil. Of the 180 students who were surveyed, 75 said they preferred using the computer. The resulting 99 percent confidence interval for the proportion of students who prefer taking notes on the computer was (0.322, 0.511). The school newspaper ran a story saying that less than half of the student body prefers taking notes on a computer. Based on the interval, is the newspaper justified in its statement?
A math teacher is investigating the problem of students losing their graphing calculators because their names aren’t written on them. In a random sample of 50 students, only 32 had their names written on their graphing calculators. The teacher constructs a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators and obtains (0.465, 0.815). What is the correct interpretation of this confidence interval?
A quality control inspector selects 12 bottles of apple juice at random from a single day’s production. The mean amount of apple juice in the bottles is 298.3 milliliters, and the 95% confidence interval for the true mean amount of juice dispensed per bottle is (296.4, 300.2). Does this interval give the quality control inspector reason to believe that the mean amount of juice in today’s bottles differs from 300 milliliters, as the juice label promises?
A college performs a survey of 424 randomly chosen graduates to estimate the proportion of alumni who are working in the field of their college degree. For example, if a student earned a degree in biology, do they work in the field of biology? Of the 424 alumni, 361 reported that they were working in the field of their college degree. A 98% confidence interval for the true proportion of graduates who are working in the field of their degree is (0.811, 0.892). What is the correct interpretation of the confidence interval?
A newspaper poll found that 54% of the respondents in a random sample of voters in the city plan to vote for candidate Roberts. A 95 percent confidence interval for the population proportion is 0.54 ± 0.06. What is the correct interpretation of the 95% confidence interval?
A study was done to estimate the mean commute time for a population of employed adults. A random sample of 25 employed adults in a particular city was taken, and the 95% confidence interval for mean commute time was calculated to be 34.42 ± 8.14 minutes. A councilman is advocating for road repairs and states that, in this city, people with jobs commute an average of 45 minutes to work each day. Does the confidence interval justify the councilman’s statement?
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