A random sample of 100 items taken from a large batch of articles contain 5 defective items. (a) Set up 96 per cent confidence limits for the proportion of defective items in the batch. (b) If the batch contains 2,669 items, set up 95% confidence interval for the proportion of defective items.
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- The American Heart Association is about to conduct in anti smoking campaign and wants to know the fraction of Americans over 35 who smoke. Suppose a sample of 1421 Americans over 35 is drawn of these people 412 smoke using the data to construct the 90% confidence interval for the population proportion of Americans over 35 who smoke.Researchers studying the spread of an insect called the hemlock woolly adelgid find that the bugs have infested 23% of a random sample of 345 hemlock trees in the study area. What's a 99% confidence interval for the population proportion of infested hemlock trees in the study area?A random sample of 120 rhesus monkeys found that the number of rhesus monkeys that live in a captive breeding facility is 77. Construct a 90% confidence interval for the true proportion of rhesus monkeys that live in a captive breeding facility.
- A researcher wants to compare the effectiveness of two different study techniques for a test. The mean test score for the first technique is 75 with a standard deviation of 5, and the mean test score for the second technique is 80 with a standard deviation of 4. The sample size for each group is 20. What is the 95% Confidence Interval for the difference in the mean test scores for the two techniques?We would like to compute a 98% confidence interval on the proportion of CBC students that will be transferring to a 4 year college or university after their time at CBC. The current proportion is unknown and we would like an error of no more than 1.5% in the estimate. How large of a sample needs to be taken?Suppose the police are able to take a SRS of cars and find that 12.3% of the cars in their sample have a safety violation with a margin of error of 2% for a 95% confidence interval. What is the confidence interval?
- A performance analyst simulated a computer system a total of 10 times, each simulation run independent of all the others. She calculated and recorded the sample means for system response time from each of the 10 runs, coming up with the following data: 2,5,17,3,9,6,4,25,8,1(a) What is the confidence interval with a 95% confidence level for the mean response time? (b) The performance analyst was concerned that the width of the confidence interval was too large, and consulted one of her colleagues (who never took simulation and modeling). He assured her that the width of the confidence interval was large because of the two large "outliers," the values 17 and 25, and that she could reduce the width of the confidence interval simply by discarding these values. She tried this, and discovered that the width of the interval did indeed go down substantially. Is this a valid method? Why or why not?We would like to compute a 95% confidence interval for the difference of proportions of men and women who are frequent binge drinkers. Of 534 males, 26% admitted to frequent binge drinking as opposed to 20.6% of 847 women. The 95% confidence interval for the difference of proportions (proportion of males - proportion of females) is (0.0179, 0.1001). Based on this confidence interval, can we conclude that men are more likely to frequently binge drink than women? (4)One scientist wondered if there was a difference in the average daily intake of dairy products between men and women. He took a sample of n1 = 50 adult men and n2 = 50 adult women and recorded their daily intake of dairy products in grams per day. A summary of the sample results is presented in the table. Construct a 95% confidence interval for the difference in the average daily intake of dairy products for men and women. Can it be concluded that there is a difference in the average daily intakes for men and women?
- You want to get a 90% confidence interval for the difference between the percentage of females with red hair compared to males with red hair. You sample 76 females and find 34 of them have red hair. You sample 65 males and find 33 have red hair. < p1−p2 <A random sample of 180 men indicated that 50 were smokers, and a random sample of 150 women surveyed indicated that 39 smoked. Construct a 98% confidence interval for the true difference in proportions of male and female smokers.Mr. Roby is trying to estimate the difference in the proportion of his male students who on average sleep fewer than 6 hours per night compared with his female students. He selects a random sample of 20 of his 75 male students and finds that 5 of them sleep fewer than 6 hours per night. He selects another random sample of 17 of his 100 female students and finds that 8 of them sleep fewer than 6 hours a night. Check the conditions for constructing a confidence interval for the difference in proportions. Random condition: A) metB) not metC) does not apply 10% condition: A) metB) not metC) does not apply Large Counts condition: A) metB) not metC) does not apply Are all the conditions for inference met? A) YesB) NoC) Not enough information