Reference no: EM13334088
An automated filling process used by a soft drink manfacturer fills bottles marked as containing 32 ounces. The amount, X, in the bottles is assumed to be a normally distributed random variable. To monitor the process, a random sample of 25 bottles is selected each day and the average amount in the bottles is computed.
1. For a particular hour, the average amount in the 25 bottles in the sample is 33.2 ounces with s=2.6 ounces. Compute a 95% confidence interval for the true average amount of soft drink in the bottles.
2. interpret the confidence interval. Can the manufacturer be certain that the actual amount going into the bottles is not 32 ounces?
3. A sample of 150 calls to a customer help line during one week found that callers were kept waiting on average for 16 minutes with s=8.
a. find the margin of error for this result if we use a 95% confidence interval for the length of time all customers during this period are kept waiting.
b. interpret for management the margin of error.
c. of we only need to be 90% confient, does the margin of error become larger or smaller?
d. find the margi of error for a 90% confidence interval.
4. click fraud has become a major concern as more and more companies advertise on the internet. when google places an ad for a company with its search results, the company pays a fee to google each time someone clicks on the link. That's fine when it's a person who's interested in buying a product or service, but not so good when it's a computer program pretending to be a customer. An analysis of 1200 clicks coming into a company's site during a week identified 175 of these clicks as fraudulent.
a. under what conditions does it make sense to treat these 1200 clicks as a sample? what would be the population?
b. show the 95% confidence interval for the population proportion of fraudulent clicks in a form suitable for sharing with a non technical audience.
c. if a company pays google $4.5 for each click, give a confidence interval (again, to presentation precision) for the mean cost due to fraud per click.
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: An automated filling process used by a soft drink manfacturer fills bottles marked as containing 32 ounces. The amount, X, in the bottles is assumed to be a normally distributed random variable. To monitor the process, a random sample of 25 bottles i..
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