Exam 9: Introduction to Hypothesis Testing

A major airline is concerned that the waiting time for customers at its ticket counter may be exceeding its target average of 190 seconds.To test this,the company has selected a random sample of 100 customers and times them from when the customer first arrives at the checkout line until he or she is at the counter being served by the ticket agent.The mean time for this sample was 202 seconds with a standard deviation of 28 seconds.Given this information and the desire to conduct the test using an alpha level of 0.02,which of the following statements is true?

A contract calls for the mean diameter of a cylinder to be 1.50 inches.As a quality check,each day a random sample of n = 36 cylinders is selected and the diameters are measured.Assuming that the population standard deviation is thought to be 0.10 inch and that the test will be conducted using an alpha equal to 0.025,what would the probability of a Type II error be?

Choosing an alpha of 0.01 will cause beta to equal 0.99.

For testing a research hypothesis,the burden of proof that a new product it is no better than the original is placed on the new product and the research hypothesis is formulated as the null hypothesis.

A local medical center has advertised that the mean wait for services will be less than 15 minutes.Given this claim,the hypothesis test for the population mean should be a one-tailed test with the rejection region in the lower (left-hand)tail of the sampling distribution.

If a hypothesis test leads to incorrectly rejecting the null hypothesis,a Type II statistical error has been made.

Explain why an increase in sample size will reduce the probability of a Type II error but will not impact the probability of a Type I error.

Aceco has a contract with a supplier to ship parts that contain no more than three percent defects.When a large shipment of parts comes in,Aceco samples n = 150.Based on the results of the sample,they either accept the shipment or reject it.If Aceco wants no more than a 0.10 chance of rejecting a good shipment,the cut-off between accepting and rejecting should be 0.0478 or 4.78 percent of the sample.

Which of the following statements is true?

In a hypothesis test,the p-value measures the probability that the alternative hypothesis is true.

A two-tailed hypothesis test with α = 0.05 is similar to a 95 percent confidence interval.

When using the p-value method for a two-tailed hypothesis,the p-value is found by finding the area in the tail beyond the test statistic,then doubling it.

If a decision maker is concerned that the chance of making a Type II error is too large,one option that will help reduce the risk is to reduce the significance level.

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces.The standard deviation is known to be 0.20 ounces.Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles,which of the following would be the correct formulation of the null and alternative hypotheses?

To calculate beta requires making a "what if" assumption about the true population parameter,where the "what-if" value is one that would cause the null hypothesis to be false.

The Adams Shoe Company believes that the mean size for men's shoes is now more than 10 inches.To test this,it has selected a random sample of n = 100 men.Assuming that the test is to be conducted using a .05 level of significance,a p-value of .07 would lead the company to conclude that its belief is correct.

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000.The best null hypothesis is:

One claim states the IRS conducts audits for not more than 5 percent of total tax returns each year.In order to test this claim statistically,the appropriate null and alternative hypotheses are: .

Type II errors are typically greater for two-tailed hypothesis tests than for one-tailed tests.

It is possible to appropriately test a null and alternative hypotheses using the test statistic approach and reach a different conclusion than would be reached if the p-value approach were used.