A machines are used for filling plastic bottles with a certain net volume. Quality engineer found that 54 of 80 bottles from Machine 1 meet the specification while 48 of 64 bottles from Machine 2 meet the specification. Construct a 95% confidence interval for the difference between the true proportion of bottles that meet the specification.
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- According to a report on sleep deprivation by the Centers for Disease Control and Prevention, the proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents. Calculate a 95% confidence interval for the difference between the proportions of Californians and Oregonians who are sleep deprived and interpret it in context of the data. Also, conduct a hypothesis, with alpha = 0.05, test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states. Construct a 95% confidence interval Which of the following correctly displays the standard error? 0.0046 0.009 0.001 0.00002 0.008An auditor of the USPS wants to examine its special two day mail handling to determine the proportion of parcels that actually arrive within the promised two day period. A randomly selected sample of 1600 such parcels is found to contain 1250 that were delivered on time. Use this to construct a 95% confidence interval for the parcels delivered on time.According to a report on sleep deprivation by the Centers for Disease Control and Prevention, the proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents. Calculate a 95% confidence interval for the difference between the proportions of Californians and Oregonians who are sleep deprived and interpret it in context of the data.
- The manager of a local fast-food restaurant is concerned about evil customers who ask for a free cup of water when placing an order, but then fill the cup with a soft drink from the beverage fountain! Themanager selects a random sample of 80 customers who asked for a water cup and found that 23 ofthose customers filled the cup with soda from the beverage fountain. Construct and interpret a 95%confidence interval for the proportion of all customers who, having asked for a cup of water whenplacing an order, will fill the cup with a soft drink from the beverage fountain. Be sure to go through theentire PANIC process.An auditor of the USPS wants to examine its special two day mail handling to determine the proportion of parcels that actually arrive within the promised two day period. A randomly selected sample of 1600 such parcels is found to contain 1250 that were delivered on time. The USPS claims that more than 75% of parcels are delivered on time. Does a 95% confidence interval support this claim?Suppose a different police department says their SRS resulted in a 95% confidence interval of 10.1% to 15.1%. What is their point estimator and margin of error?
- In order to judge the effectiveness of an advertising campaign for a certain brand of pretzel, a company obtained a simple random sample of 80 convenience store receipts the week before the ad campaign began, found that 16 of them showed a purchase of the pretzels. Another simple random sample of 50 receipts was taken the week after the ad campaign and 28 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. Let p1 be the population proportion of convenience store receipts showed a purchase of the pretzels taken in the week before the ad campaign began, and p2 be the population proportion of convenience store receipts showed a purchase of the pretzels taken in the week after the ad campaign. •Find the point estimate. •Find the standard error. Round to four decimal places. •Find the margin of error. Round to four decimal places.In order to judge the effectiveness of an advertising campaign for a certain brand of pretzel, a company obtained a simple random sample of 80 convenience store receipts the week before the ad campaign began, found that 16 of them showed a purchase of the pretzels. Another simple random sample of 50 receipts was taken the week after the ad campaign and 28 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. Let p1 be the population proportion of convenience store receipts showed a purchase of the pretzels taken in the week before the ad campaign began, and p2 be the population proportion of convenience store receipts showed a purchase of the pretzels taken in the week after the ad campaign. 1. Find the point estimate. 2. Find the standard error. Round to four decimal places. 3. Find the margin of error. Round to four decimal places.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?
- 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:According to a report on sleep deprivation by the Centers for Disease Control and Prevention, the proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this percent is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents. Suppose we want to calculate a 99% confidence interval for the difference between the proportions of Californians and Oregonians who are sleepdeprived. 1. State the critical value for the interval (3 decimal places): 2. State the difference between the sample proportions, POregon-PCalifornia (3 decimal places): 3. State the standard error of the difference between the proportions (3 decimal places): 4. State the confidence interval being sure to use proper notation (3 decimal places each):A recent survey showed that from a sample of 500 packages delivered by a Postal Service,480 were delivered on time.a) Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service. b) The manager of the Postal Services claims that 98 percent of their mail are delivered on time. Test at the 1% significance level to determine whether the true proportion is less than 98 percent.