A restaurant has a jar of red and white gumballs by the cash register, and invites customers to guess the proportion of red gumballs. Of the 55 gumballs that you can see, you count 34 red ones. Give a 90% confidence interval for the proportion of red gumballs in the jar, using the large-sample method. [ Select ] Suppose you had counted 49 red gumballs out of 55. Why would a plus-four confidence interval be preferable to a large-sample confidence interval in that case? [ Select ]
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- What is meant by the sample space of an experiment?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:In a recent Zogby International Poll, nine of 48 respondents rated the likelihood of a terrorist attack in their community as “likely” or “very likely”. Use the “plus four” method to create a 98% confidence interval for the proportion of American adults who believe that a terrorist attack in their community is likely or very likely. Interpret your confidence interval.
- In a random sample of 50 patients undergoing a standard surgical procedure, 15 required medication for post operative pain. In a random sample of 90 patients undergoing a new procedure, only 16 required pain medication. a)Are conditions met to perform inference onthis study? b)Construct and interpret a 95% confidence interval for the difference in the proportions of patients needing pain medication between the old and new procedures. c) A physician claims that the proportion of patients who need pain medication is the same for both procedures. Does the confidence interval contradict this claim? Why/Why not?A sample of 250 items from lot A contains 10 defective items, and a sample of 300 itemsfrom lot B is found to contain 18 defective items. Construct a 98% confidence interval for the difference of proportions of defective items.In order to judge the effectiveness of an advertising campaign for a certain brand of pretzel, a company obtained a simple random sample of 95 convenience store receipts the week before the ad campaign began, and found that 28 of them showed a purchase of the pretzels. Another simple random sample of 65 receipts was taken the week after the ad campaign, and 33 of them showed a pretzel purchase. Construct a 98% confidence interval for the difference between the proportions of customers purchasing pretzels before and after the ad campaign. Interpret the results. A marketing manager claims that the proportion of customers who purchased pretzels did not change after the ad campaign. Does the confidence interval contradict this claim?
- A telephone company has the business objective of wanting to estimate the proportion of households that would purchase an additional telephone line if it were made available at a reduced installation cost. Data is collected from a random sample of 500 households. The results indicate that 135 of the households would purchase the additional telephone line at a reduced installation cost. - construct a ninety nine percent confidence interval estimate for the population proportion of households that would purchase the additional telephone line.During a flu vaccine shortage in the United States, less than a majority of people were able to receive the vaccine. The results of a survey given to a random sample of 2,350 vaccine-eligible people indicated that 978 of the 2,350 people had received flu vaccine. a) Construct and interpret a 95 percent confidence interval for the proportion of vaccine-eligible people who had received flu vaccine.A new television series must prove that it has more than 25% of the viewing audience after its initial 13-week run in order to be judged successful. Assume that in a sample of 400 households, 112 were watching the series. (b) Find a 99% confidence interval for the proportion of the viewing audience after its initial 13-week run
- A farmer wants to test the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries. Of a random sample of 100 blooms,77 yield marketable strawberries. Is this evidence that two-thirds or more of all blooms grown with this pest control method ends up as marketable strawberries? The 95% large-sample confidence interval for the proportion of blooms that yield marketable strawberries is?In a random sample of 190 adults (ages 21-30), it was found that 70% of them have received speeding tickets. Based on this data, what would be the 90% confidence interval of the true proportion of young adults who have received speeding tickts?in a random sample of 800 austin automobile owners, it was found that 480 would like to see the size of the cars reduced. A 95% confidence interval for the proportion of all austin car owners who would like to see another car is: a) (0.532, 0.667) b) (0.572, 0.628) c) (0.566, 0.634)