Exam 9: Hypothesis Testing

It is estimated that the average person in the United States uses 123 gallons of water per day.Some environmentalists believe this figure is too high and conduct a survey of 40 randomly selected Americans.They find a mean of 113.03 gallons and a population standard deviation of 25.99 gallons.Calculate the p-value for this test statistic,and test the hypothesis at α = .01.

A company has developed a new ink-jet cartridge for its printer that it believes has a longer lifetime on average than the one currently being produced.To investigate its length of life,240 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce.The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages,respectively.The historical average lifetime for cartridges produced by the current process is 1502.5 pages.At α = .05,test the claim that the new cartridge has a longer lifetime.

The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription.The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions.To test her theory,she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle.She finds a sample mean of 61.35.Assume a population standard deviation of 4.45.If we want the probability of a Type I error and Type II error to be equal to .05,what is the sample size needed to make both the probability of a Type I error and the probability of a Type II error as small as possible.(Assume an alternate value of the population mean of 61. )The claim is that the tablet count is different from 60.

A null hypothesis H₀: μ ≥ 2.4 is not rejected at a significance level of 0.04.(α = 0.04).The standard deviation for the normally distributed population is known to be 0.40.Determine the Type II error,if we assume that the actual mean is 2.125 based on a sample size of 16.

In a study of distances traveled by buses before the first major engine failure,a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles.Calculate the appropriate test statistic to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

We are testing H₀: p ? .7;versus H_A: p < .7.With $\hat { p } = .63$ and n = 100,at ? = .01,we do not reject the null hypothesis.

In a bottling process,a manufacturer will lose money if the bottles contain either more or less than is claimed on the label.Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant-size bottle differs from the labeled amount of 20 ounces.The manager samples nine bottles,measures their contents,and finds the sample mean is 19.7 ounces and the sample standard deviation is 0.3 ounces.Calculate the appropriate test statistic to test the hypotheses.

A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards.The mean emission of all converters of this type must be less than 20 parts per million of carbon.Ten (10)converters are manufactured for testing purposes and their emission levels are measured,with a mean of 17.17 and a standard deviation of 2.98.Test the hypotheses at α = .01.

When testing a hypothesis about a single mean,a sample size of 200 is selected from a normally distributed population.If the population standard deviation is known,the correct test statistic to use is ___________.

The power of a statistical test is the probability of rejecting the null hypothesis when it is false.

Last year,during an investigation of the time spent reading emails on a daily basis,researchers found that on Monday the average time was 50 minutes.Office workers claim that with the increased spam and junk mail,this time has now increased.To conduct a test,a sample of 25 employees is selected,with the following results: sample mean = 51.05 minutes and sample standard deviation = 14.2 minutes.What is the critical value for α = .05 to test the hypotheses and conduct a test to determine if the null hypothesis can be rejected.

A microwave manufacturing company has just switched to a new automated production system.Unfortunately,the new machinery has been frequently failing and requiring repairs and service.The company has been able to provide its customers with a completion time of 6 days or less.To analyze whether the completion time has increased,the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days.At a significance level of .10,we can show that the completion time has increased.

The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually average 1 gallon.It is known from the manufacturer's specifications that the standard deviation of the amount of water is equal to 0.02 gallon.A random sample of 32 bottles is selected,and the mean amount of water per 1-gallon bottle is found to be 0.995 gallon.Calculate a confidence interval to test the hypotheses at α = .001.

If a null hypothesis is rejected at a significance level of .05,it will _____________ be rejected at a significance level of .01

One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25 percent of leases in Atlanta.Suppose a US car manufacturer conducts its own survey in an effort to determine whether this figure is correct.Of the 384 leases in Atlanta surveyed,79 lease a Lexus.Calculate the p-value associated with the test statistic,and test the claim at α = .05.

For the following hypothesis test,where H₀: μ ≤ 10;vs.H_A: μ > 10,we reject H₀ at level of significance α and conclude that the true mean is greater than 10,when the true mean is really 14.Based on this information,we can state that we have:

The ____________ hypothesis is not rejected unless there is sufficient sample evidence to do so.

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.The alternative hypothesis is:

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.What is the critical value to test the claim at α = .01?

The larger the p-value,the more we doubt the null hypothesis.