Exam 9: Introduction to Hypothesis Testing

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?

When using the p-value method,the null hypothesis is rejected when the calculated p-value > α.

For the following hypothesis: With n = 20, = 71.2,s = 6.9,and α = 0.1,state the conclusion.

The following is an appropriate statement of the null and alternate hypotheses for a test of a population mean: H₀ : μ < 50 H_A : μ > 50

Type II error is failing to reject the null hypothesis when the null is actually false.

For the following hypothesis test: With n = 80,σ = 9,and = 47.1,state the calculated value of the test statistic z.

At a recent meeting,the manager of a national call center for a major Internet bank made the statement that the average past-due amount for customers who have been called previously about their bills is now no larger than $20.00.Other bank managers at the meeting suggested that this statement may be in error and that it might be worthwhile to conduct a test to see if there is statistical support for the call center manager's statement.The file called Bank Call Center contains data for a random sample of 67 customers from the call center population.Assuming that the population standard deviation for past due amounts is known to be $60.00,what should be concluded based on the sample data? Test using α = 0.10.

For the following hypothesis: With n = 20, = 71.2,s = 6.9,and α = 0.1,state the calculated value of the test statistic t.

The manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly more than 3 minutes.A random sample of 100 customers was taken.The average length of calling time in the sample was 3.1 minutes with a standard deviation of 0.5 minutes.At a 0.05 level of significance,it can be concluded that the mean of the population is:

A national car rental chain believes that more than 80 percent of its customers are satisfied with the check-in process that the company is using.To test this,a random sample of n = 200 customers are surveyed.These sample results show 168 that say they were satisfied.If the test is to be conducted using a .05 level of significance,what is the critical value?

A sample is used to obtain a 95 percent confidence interval for the mean of a population.The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20,the null hypothesis could be rejected at a level of significance of 0.05.

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

The police chief in a local city claims that the average speed for cars and trucks on a stretch of road near a school is at least 45 mph.If this claim is to be tested,the null and alternative hypotheses are: H₀ : μ < 45 mph H_a : μ ≥ 45 mph

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?

An article in an operations management journal recently stated that a formal hypothesis test rejected the hypothesis that mean employee productivity was less than $45.70 per hour in the wood processing industry.Given this conclusion,it is possible that a Type I statistical error was committed.

The null and alternate hypotheses must be opposites of each other.

If the probability of a Type I error is set at 0.05,then the probability of a Type II error will be 0.95.

According to CNN business partner Careerbuilder.com,the average starting salary for accounting graduates in 2008 was at least $47,413.Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2008. Compute the power of the hypothesis test to reject the null hypothesis if the true average starting salary is only $47,000.Assume that the population standard deviation is known to be $4,600 and the test is to be conducted using an alpha level equal to 0.01.

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

A local medical center has advertised that the mean wait for services will be less than 15 minutes.In an effort to test whether this claim can be substantiated,a random sample of 100 customers was selected and their wait times were recorded.The mean wait time was 17.0 minutes.Based on this sample result,there is sufficient evidence to reject the medical center's claim.