Exam 9: Statistical Inferences Based on Two Samples

Sandwiches sold at a local grocery store claim to have 6 grams of fat per sandwich.Ten sandwiches are brought with results of a mean of 5.93g of fat and a standard deviation of 0.13g.If fat content is normally distributed,the 99% confidence interval for the true fat content would be _____.

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are current (between 0 and 60 days after billing).The historical records show that over the past 8 years,70 percent of the accounts have been current.The sample size needed in order to be 99% confident that the sample proportion of the current customer accounts is within .03 of the true proportion of all current accounts for this company would be _____.

All other things being constant,the margin of error for a confidence interval for a population mean increases as the sample size decreases.

Failure to meet payments on student loans has been a major problem for both banks and the government.A random sample of 350 loans to students indicates that 147 are in default.The 99% confidence interval for the true proportion of loans in default is _____.

You want to estimate the proportion of customers who are satisfied with their supermarket at α = .10 to within .025 of the true value.It has been estimated that p =.85.How large of a sample is needed?

We want to estimate with 99 percent confidence the percentage of buyers of cars who are under 30 years of age.A margin of error of 5 percentage points is desired.What sample size is needed?

A machine has been designed to make nails which are 8cm long with a standard deviation of 0.15cm.A sample of 48 nails is selected periodically to assess if the length is too variable from the standard of 8cm.From the sample of 48 nails,the mean is found to be 7.983cm.Assume the lengths are normally distributed and the standard deviation is known to be 0.15cm.Compute the 95% confidence interval for the population mean nail length.

Provide a one-sentence interpretation of the 95% confidence interval for the average change in completion time.

Consider a normally distributed population with unknown standard deviation.When computing a confidence interval for the population mean,the values $t _ { \alpha / 2 }$ And $z _ { \alpha / 2 }$ Will be close in value when

In a random sample of 651 computer scientists who subscribed to a web-based daily news update,it was found that the average salary was $46,816 with a standard deviation of $12,557.A 91% confidence interval for the mean salary of computer scientists would be _____.

In 2007,13,000 internet users were surveyed and asked about their willingness to pay fees for access to websites.Of these,2,938 were definitely not willing to pay such fees.The 95% confidence interval for the proportion definitely unwilling to pay fees would be _____.

What sample size is needed to obtain a 95 percent confidence interval for the proportion of fat in meat that is within 2 percent of the true value?

Let p₁ represent the population proportion of Canadian women who are in favour of a new modest tax on "junk food".Let p₂ represent the population proportion of Canadian men who are in favour of a new modest tax on "junk food".Out of the 265 women surveyed,106 of them are in favour of a "junk food" tax.Out of the 285 men surveyed,only 57 of them are in favour a "junk food" tax. -Interpret the 95% confidence interval for the difference between p₁ and p₂.

The 99% confidence interval for the average weight of a product is from 71.36kg to 78.64kg.Interpret this confidence interval.

An insurance analyst working for a car insurance company would like to determine the proportion of accident claims covered the company.A random sample of 200 claims shows that the insurance company covered 80 accident claims while 120 claims were not covered.Construct a 90% confidence interval estimate of the true proportion of claims covered by the insurance company.

As the sample size n increases,the width of the confidence interval for a population mean or proportion _______________.

A granola bar manufacturer states that their granola bars contain 28 grams of carbohydrates per bar.A sample of five granola bars is tested and a mean of 28.2g is obtained with a standard deviation of 2.7g.If carbohydrate content is normally distributed,how many granola bars should be tested to estimate the true mean grams of carbohydrates per bar to within 0.5g with 99% confidence?

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,the 98% confidence interval for the mean weight of all such candy would be _____.

When constructing a confidence interval for a sample proportion,the t distribution is appropriate if the sample size is small.

There are an average of 22.455 employees at 22 office furniture dealers in a province with a standard deviation of 18.52.If the number of employees can be approximated by a normal distribution,the 99% confidence interval for the true mean number of full-time employees at office furniture dealers would be _____.