Exam 9: Introduction to Hypothesis Testing

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 "accept" the claimed mileage for this car?

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?

When the hypothesized proportion is close to 0.50,the spread in the sampling distribution of p is greater than when the hypothesized proportion is close to 0.0 or 1.0.

A hypothesis test is to be conducted using an alpha = .05 level.This means:

The probability of a Type II error decreases as the "true" population value gets farther from the hypothesized population value,given that everything else is held constant.

Lube-Tech is a major chain whose primary business is performing lube and oil changes for passenger vehicles.The national operations manager has stated in an industry newsletter that the mean number of miles between oil changes for all passenger cars exceeds 4,200 miles.To test this,an industry group has selected a random sample of 100 vehicles that have come into a lube shop and determined the number of miles since the last oil change and lube.The sample mean was 4,278 and the sample standard deviation was 780 miles.Based on this information,the test statistic is approximately t = 1.000.

A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course.To test this,a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test.These students will take the company's course and then retake the SAT test.Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05,find the critical value in terms of improvement in SAT points,which would be needed prior to finding a beta.

A company makes a device that can be fitted to automobile engines to improve the mileage.The company claims that if the device is installed,owners will observe a mean increase of more than 3.0 mpg.Assuming that the population standard deviation of increase is known to be 0.75 mpg,and a sample of size 64 cars is selected with an = 3.25 mpg,use the p-value approach to test the null hypothesis using a significance level of 0.05.

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:

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.

A major package delivery company claims that at least 95 percent of the packages it delivers reach the destination on time.As part of the evidence in a lawsuit against the package company,a random sample of n = 200 packages was selected.A total of 188 of these packages were delivered on time.Using a significance level of .05,the test statistic for this test is approximately z = -0.65.

Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent.A random sample of 100 students was taken.Fifty-five of them favored Mike.At a 0.05 level of significance,it can be concluded that the proportion of the students in favor of Mike

Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures and share little in common with each other.

In a hypothesis test involving a population mean,which of the following would be an acceptable formulation?

Of the two types of statistical errors,the one that decision makers have most control over is Type I error.

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

A cell phone company believes that 90 percent of their customers are satisfied.They survey a sample of n = 100 customers and find that 82 say they are satisfied.In calculating the standard error of the sampling distribution (σ_p)the proportion to use is 0.82.

The executive director of the United Way believes that more than 24 percent of the employees in the high-tech industry have made voluntary contributions to the United Way.In order to test this statistically,the appropriate null and alternative hypotheses are: .

A small city is considering breaking away from the county school system and starting its own city school system.City leaders believe that more than 60 percent of residents support the idea.A poll of n = 215 residents is taken and 134 people say they support starting a city school district.Using a 0.10 level of significance,conduct a hypothesis test to determine whether this poll supports the belief of city leaders.

In a hypothesis test,increasing the sample size will generally result in a smaller chance of making a Type I error since sampling error is likely to be reduced.