Exam 9: One-Sample Hypothesis Tests

After lowering the landing gear,the pilot notices that the "gear down and locked" light is not illuminated."It's probably just a burned out light bulb," she says,as she proceeds on final approach for landing.Considering the pilot's hypothesis,which is the result of Type I error?

A two-tailed hypothesis test

The p-value is the probability of obtaining the sample result (or one more extreme),assuming H0 is true.

The critical value in a hypothesis test

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.The test statistic to find out whether the percentage has risen would be

For a sample of nine items,the critical value of Student's t for a left-tailed test of a mean at α = .05 is −1.860.

Which is a valid null hypothesis?

In hypothesis testing,we are trying to reject the alternative hypothesis.

Pedro hypothesizes that more than half of his classmates would prefer a virtual web graduation ceremony,rather than sitting in the hot sun during the commencement speech.He takes a random sample of his classmates and performs a test.The results shown below are from MegaStat.What would Pedro conclude from this test? Explain carefully.

"I believe your airplane's engine is sound," states the mechanic."I've been over it carefully,and can't see anything wrong.I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500.But I believe that roughness you heard in the engine on your last flight was probably just a bit of water in the fuel,which passed harmlessly through the engine and is now gone." As the pilot considers the mechanic's hypothesis,the cost of Type I error is

A simultaneous reduction in both α and β will require a larger sample size.

For a given level of significance,the critical value of Student's t increases as n increases.

In a test of a mean,the reported p-value is .025.Using α = .05 the conclusion would be to

The critical value of a hypothesis test is based on the researcher's selected level of significance.

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours.A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours."Aha!" she cried,"the average stay exceeds the guideline." The p-value for a right-tailed test of her hypothesis is

Why is it better to say "fail to reject H0" instead of "accept H0"?

The process that produces Sonora Bars (a type of candy)is intended to produce bars with a mean weight of 56 gm.The process standard deviation is known to be 0.77 gm.A random sample of 49 candy bars yields a mean weight of 55.82 gm.Find the p-value for a test to see whether the candy bars are smaller than they are supposed to be.

Given a normal distribution with σ = 3,we want to test the hypothesis H0: μ = 20.We find that the sample mean is 21.The test statistic is

Last year,10 percent of all teenagers in Greenville purchased a new iPhone.This year,a sample of 260 randomly chosen Greenville teenagers showed that 39 had purchased a new iPhone.To test whether the percentage has risen,the critical value at α = .05 is

Which is not a step in hypothesis testing?