Exam 9: Hypothesis Testing

When conducting a hypothesis test about a single mean,other relevant factors held constant,increasing the level of significance α from .05 to .10 will reduce the probability of a Type II error.

A cereal manufacturer is concerned that the boxes of cereal not be underfilled or overfilled.Each box of cereal is supposed to contain 13 ounces of cereal.A random sample of 31 boxes is tested.The average weight is 12.58 ounces,and the standard deviation is 0.25 ounces.What is the critical value for testing the hypotheses at α = .001.

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.

A Type I error is rejecting a true null hypothesis.

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

The manager of a local specialty store is concerned with a possible slowdown in payments by her customers.She measures the rate of payment in terms of the average number of days receivables are outstanding.Generally,the store has maintained an average of 50 days with a standard deviation of 10 days.A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days.Calculate the appropriate test statistic to test the hypotheses.

We are testing H₀: p ≥ .7;versus H_A: p< .7.With = .63 and n = 100,at α = .01,we do not reject the null hypothesis.

In testing H₀: μ = 23;versus H_A: μ > 23,when = 26,s = 6,and n = 20,what is the value of the test statistic?

A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month.Historical data shows that on average 18 percent of the company airplanes have arrived late.In a random sample of 1,240 airplanes,310 airplanes have arrived late.If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased,what is the value of the calculated test statistic?

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 ___________.