Exam 9: Hypothesis Testing

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night.If this is to happen,it will have to move one of its most viewed shows to another slot.The network conducts a survey asking its viewers which show they would rather watch.The network receives 827 responses,of which 428 indicate that they would like to see the new show in the lineup.At the 1% significance level,the rejection region(s)for this hypothesis would be ________.

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.At the 5% significance level,the decision is to ___________.

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later,School Buses Still Late," Boston Globe,October 5,2011).Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route.Historically,the bus service on the route has been,on average,12 minutes late.After the schedule adjustment,the first 36 runs were an average of eight minutes late.As a result,the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late.Assume a population standard deviation for bus arrival time of 12 minutes.At the 5% significance level,does the evidence support the Boston public school district's claim?

When conducting a hypothesis test concerning the population mean,and the population standard deviation is unknown,the value of the test statistic is calculated as __________.

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.At a 5% significance level,the critical value(s)is(are)___________.

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.To determine whether there has been a decrease in the average number of customers visiting the dealership daily,the appropriate hypotheses are _________.

For a given sample size,any attempt to reduce the likelihood of making one type of error (Type I or Type II)will increase the likelihood of the other error.

To test if the mean IQ of employees in an organization is greater than 100,a sample of 30 employees is taken and the value of the test statistic is computed as t₂₉ = 2.42 If we choose a 5% significance level,we _____________.

A Type I error occurs when we ___________.

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential.In 2009,the high school dropout rate was 8.1%.A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts.The polling company would like to determine whether the dropout rate has decreased.At a 5% significance level,the decision is to ____________.

A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean

When conducting a hypothesis test concerning the population mean,and the population standard deviation is known,the value of the test statistic is calculated as _________.

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.The value of the test statistic is ____________.

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups.He knows that the long-run average markup in his lot is $5,600.He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800.Assume the markups are normally distributed.What is the value of an appropriate test statistic for the car dealer to use to test his claim?

What is the decision rule when using the p-value approach to hypothesis testing?

Which of the following represents an appropriate set of hypotheses?

What type of data would necessitate using a hypothesis test of the population proportion rather than a test of the population mean?

A university wants to know if the average salary of its graduates has increased since 2010.The average salary of graduates prior to 2010 was $48,000.Since 2010,the university surveyed 256 graduates and found an average salary of $48,750.Assume that the standard deviation of all graduates' salaries is $7,000. a.Specify the null and alternative hypotheses to determine whether the average salary of graduates has increased. b.Calculate the value of the test statistic and the critical value at a 5% significance level. c.At the 5% significance level,can you conclude that salaries have increased? Explain.

As a general guideline,we use the alternative hypothesis as a vehicle to establish something new,or contest the status quo,for which a corrective action may be required.

A one-tailed hypothesis test of the population mean has ______________.