Exam 9: Statistical Inferences Based on Two Samples

In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3cm with a standard deviation of .3cm.Assuming bolt length is normally distributed,what is the 95% confidence interval for the true mean length of the bolt?

It is appropriate to compute a confidence interval for a population proportion p if $n \hat { p }$ and $n ( 1 - \hat { p } )$ are both at least 5.

A manufacturer of soft dog treats establishes that,on average,13.5% of each treat contains "crude protein",with a standard deviation of $\sigma$ = 0)1%.When the process machine is properly calibrated,then this value is maintained,but uncontrollable factors such as moisture levels can alter the crude protein percentage.For quality control purposes,the manufacturer wishes to estimate the mean crude protein percentage to within 0.025% of its true value with a 99% confidence.If the percentage of "crude protein" is normally distributed,what sample size should be used?

What sample size is needed to estimate the proportion of highway speeders within 5 percent using a 90 percent confidence level?

Unoccupied seats on flights cause airlines to lose revenue.Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year.225 flight records are randomly selected and the number of unoccupied seats is noted with a sample mean of 11.6 seats and a standard deviation of 4.1 seats.A 90% confidence interval for $\mu$ ,the mean number of unoccupied seats per flight during the past year would be _____.

In a survey of 308 adults,17 listed jewellery among the romantic gifts men want to receive.The 98% confidence interval for the proportion of all adults who include jewellery among their responses would be _____.

A marketing research company surveyed grocery shoppers in the east and west coasts to see the percentage of the customers who prefer chicken to other meat.The data are given below. Sample size Number of customers in the sample that prefer chicken East Coast 492 156 West Coast 386 172 -Provide a one-sentence interpretation of this interval.

A local company makes a candy that is supposed to weigh 1.00 gram.A random sample of 25 pieces of candy produces a mean of 0.996g with a standard deviation of 0.004g.If candy weight is normally distributed,how many pieces of candy must we sample if we want to be 99% confident that the sample mean is within 0.001g of the true mean?

In a manufacturing process,we are interested in measuring the average length of a certain type of bolt.Past data indicates that the lengths are normally distributed with standard deviation 0.25cm.How many bolts should be sampled in order to make us 95% confident that the sample mean bolt length is within 0.02cm of the true mean bolt length?

Scores on a standard IQ test are normally distributed with population standard deviation 15.How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of 0.5)and we want 97% confidence in the results?

What sample size is needed to estimate with 95 percent confidence the mean intake of calcium within 20 units of the true mean if the intake is normal with a variance of 1900 units?

In determining the sample size to estimate a population proportion,as p approaches 0.5,the calculated value of the sample size ______________.

A researcher is investigating the popularity of new packaging for a product.In a random sample of 300 people from Toronto,63 preferred the new packaging.Of 400 people from Montreal,52 preferred the new packaging.Find a 90 percent confidence interval for the difference between the proportions of people who prefer the new packaging in Toronto and Montreal.

An auditor was hired to verify the accuracy of a company's new billing system.Thirty-five (35)invoices produced since the system was installed were sampled.The average error on the invoices was $1.00.Historically,the population standard deviation is around $124.00.A 97% confidence interval for the mean error per invoice would be _____.

A confidence interval for the population mean is an interval constructed around the _____.

The weight of a product is normally distributed.A sample of 50 units is taken from a batch.The sample yielded the following results: $\bar { x }$ = 75kg and s = 10kg. -Calculate a 95 percent confidence interval for $\mu$ .

A golf tournament organizer is attempting to estimate the average number of strokes for the 13^th hole on a given golf course.On a particular day,64 players completed the play on the 13^th hole with average of 4.25 strokes and standard deviation of 1.6 strokes.Assuming the number of strokes can be approximated by a normal distribution,determine the 95% confidence interval for the average number of strokes.

Ten items of 100 are defective.Develop a 95 percent confidence interval for the population proportion of defectives.

When constructing a confidence interval for a population mean,if the population is normally distributed with unknown standard deviation and the sample size is 10,then the distribution of $\bar { x }$ Is based on _____ distribution.

A computer manufacturing company has sent a mail survey to 2800 of its randomly selected customers that have purchased the recently launched personal computer.The survey asked the customers whether or not they were satisfied with the computer.800 customers responded to the survey.640 customers indicated that they were satisfied,while 160 customers indicated they were not satisfied with their new computer.Construct a 96% confidence interval estimate of the true proportion of customers satisfied with their new computer.