Exam 9: Hypothesis Testing

It has been hypothesized that on average employees spend one hour a day playing video games at work.To test this at her company,a manager takes a random sample of 35 employees,who showed a mean time of 55 minutes per day,with an assumed population standard deviation of 5 minutes.Calculate the test statistic.

If a null hypothesis is rejected at a significance level of .01,it will ____________ be rejected at a significance level of .05.

____________ is the probability of not rejecting H₀ when H₀ is false.

It has been hypothesized that on average employees spend one hour a day playing video games at work.To test this at her company,a manager takes a random sample of 35 employees,who showed a mean time of 55 minutes per day with an assumed population standard deviation of 5 minutes.Calculate a confidence interval to test the hypotheses that the employees spend a different amount of time from one hour (60 minutes)at α = .02 and interpret.

In an early study,researchers at Ivy University found that 33 percent of the freshmen had received at least one A in their first semester.Administrators are concerned that grade inflation has caused this percentage to increase.In a more recent study,of a random sample of 500 freshmen,185 had at least one A in their first semester.Calculate the p-value associated with the test statistic and test the claim at α = .05.

A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards.The mean emission of all converters of this type must be less than 20 parts per million of carbon.Ten (10)converters are manufactured for testing purposes and their emission levels are measured,with a mean of 17.17 and a standard deviation of 2.98.Calculate the appropriate test statistic to test the hypotheses.

According to a national survey,the average commuting time for people who commute to a city with a population of 1 to 3 million is 19.0 minutes.Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim in her city.Taking a random sample of 20 commuters,she calculates a mean time of 19.346 minutes and a standard deviation of 2.842 minutes.Calculate the appropriate test statistic to test the hypotheses.

In 1930,the average size of a public restroom was 172 square feet.By 1990,due to federal disability laws,the average size had increased to 471 square feet.Suppose that a design team believes that this standard has increased from the 1990 level.They randomly sample 23 public restrooms in a major midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94.Test 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,40 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.Calculate the appropriate test statistic to test the hypotheses.

It is estimated that the average person in the United States uses 123 gallons of water per day.Some environmentalists believe this figure is too high and conduct a survey of 40 randomly selected Americans.They find a mean of 113.03 gallons and a population standard deviation of 25.99 gallons.Calculate the appropriate test statistic to test the hypotheses.

Assuming a fixed sample size,as α (Type I error)decreases,β (Type II error)___________.

If a two-sided null hypothesis is rejected for a single mean at a given significance level,the corresponding one-sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will ______________ be rejected at the same significance level.

If a null hypothesis is not rejected at a significance level of .05,it will _____________ be rejected at a significance level of .01.

It can be established at α = .05 that a majority of students favor the plus/minus grading system at a university if in a random sample of 500 students,270 favor the system.

In a study of distances traveled by buses before the first major engine failure,a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles.Calculate the p-value corresponding to the test statistic used to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles,and determine if the null hypothesis can be rejected at α = .01.

A mail-order business prides itself in its ability to fill orders in less than six calendar days,on average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.On one occasion when a sample of 39 orders was selected,the average number of days was 6.65 with a population standard deviation of 1.5 days.What is the critical value for α = .10 to test the hypothesis that the time to fill is less than 6 days?

In an early study,researchers at Ivy University found that 33 percent of the freshmen had received at least one A in their first semester.Administrators are concerned that grade inflation has caused this percentage to increase.In a more recent study,of a random sample of 500 freshmen,185 had at least one A in their first semester.Calculate the appropriate test statistic to test the hypotheses.

The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription.The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions.To test her theory,she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle.She finds a sample mean of 61.35.Assume a population standard deviation of 4.45.If we have preset the probability of a Type I error equal to .05,compute the probability of a Type II error.(Assume an alternative value of the population mean of 61. )The claim is that the tablet count is different from 60.

Alpha (α)is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.

The value of the test statistic is compared with a(n)_______________ in order to decide whether the null hypothesis can be rejected.