Exam 9: Introduction to Hypothesis Testing

Which of the following statements is true?

Suppose a recent random sample of employees nationwide that have a 401(k)retirement plan found that 18% of them had borrowed against it in the last year.A random sample of 100 employees from a local company who have a 401(k)retirement plan found that 14 had borrowed from their plan.Based on the sample results,is it possible to conclude,at the α = 0.025 level of significance,that the local company had a lower proportion of borrowers from its 401(k)retirement plan than the 18% reported nationwide?

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.

A large tire manufacturing company has claimed that its top line tire will average more than 80,000 miles.If a consumer group wished to test this claim,they would formulate the following null and alternative hypotheses: H₀ : μ ≥ 80,000 H_α : μ ≠ 80,000

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.

The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces.Every box of cereal is not expected to contain exactly the targeted weight,but the average of all boxes filled should.At the end of every shift (eight hours),16 boxes are selected at random and the mean and standard deviation of the sample are computed.Based on these sample results,the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate.Use α = 0.05.Establish the appropriate null and alternative hypotheses to be tested for boxes that are supposed to have an average of 24 ounces.

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.

The critical value in a null hypothesis test is called alpha.

A report recently published in a major business periodical stated that the average salary for female managers is less than $50,000.If we were interested in testing this,the following null and alternative hypotheses would be established: H₀ : μ ≥ 50,000 H_α : μ < 50,000

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,how large could the sample mean be before they would reject the null hypothesis?

A major airline has stated in an industry report that its mean onground time between domestic flights is less than 18 minutes.To test this,the company plans to sample 36 randomly selected flights and use a significance level of 0.10.Assuming that the population standard deviation is known to be 4.0 minutes,the probability that the null hypothesis will be "accepted" if the true population mean is 16 minutes is approximately 0.955.

After completing sales training for a large company,it is expected that the salesperson will generate a sale on at least 15 percent of the calls he or she makes.To make sure that the sales training process is working,a random sample of n = 400 sales calls made by sales representatives who have completed the training have been selected and the null hypothesis is to be tested at 0.05 alpha level.Suppose that a sale is made on 36 of the calls.Based on these sample data,which of the following is true?

Waiters at Finegold's Restaurant and Lounge earn most of their income from tips.Each waiter is required to "tip-out" a portion of tips to the table bussers and hostesses.The manager has based the "tip-out" rate on the assumption that the mean tip is at least 15% of the customer bill.To make sure that this is the correct assumption,he has decided to conduct a test by randomly sampling 60 bills and recording the actual tips. State the appropriate null and alternative hypotheses.

The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year.To test her hypothesis,she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750.State the appropriate null and alternative hypotheses.

The Gordon Beverage Company bottles soft drinks using an automatic filling machine.When the process is running properly,the mean fill is 12 ounces per can.The machine has a known standard deviation of 0.20 ounces.Each day,the company selects a random sample of 36 cans and measures the volume in each can.They then test to determine whether the filling process is working properly.The test is conducted using a 0.05 significance level.What is the critical value in ounces?

The loan manager for State Bank and Trust has claimed that the mean loan balance on outstanding loans at the bank is over $14,500.To test this at a significance level of 0.05,a random sample of n = 100 loan accounts is selected.Assuming that the population standard deviation is known to be $3,000,the value of that corresponds to the critical value is approximately $14,993.50.

A consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level.They plan to test the hypothesis using a significance level of 0.05 and a sample size of n = 100 cars.It is believed that the population standard deviation is 3 mpg.Based upon this information,if the "true" population mean is 32.0 mpg,what is the probability that the test will lead the consumer group to reject the claimed mileage for this car?

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

The R.D.Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice.When the machine is running properly,the average number of fluid ounces in the cup should be 14.Periodically the machines need to be tested to make sure that they have not gone out of adjustment.To do this,six cups are filled by the machine and a technician carefully measures the volume in each cup.In one such test,the following data were observed: Which of the following would be the correct null hypothesis if the company wishes to test the machine?

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: H₀ : μ ≤ 0.05 H_a : μ > 0.05