Exam 9: Hypothesis Testing

George W.Bush famously claimed in his 2003 State of the Union address that the United States had uncovered evidence that Iraq had developed weapons of mass destruction under Saddam Hussein.Consider the null hypothesis,"Iraq does not possess weapons of mass destruction." After deciding that Iraq did possess weapons of mass destruction and invading this country,the United States found no evidence of said weapons.Is this a Type I or a Type II error on the part of the United States? Explain.

A schoolteacher is worried that the concentration of dangerous,cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L.At a 5% significance level,the decision is to ________________________________________________.

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000.A random sample of 34 students had an average debt load of $18,200.It is believed that the population standard deviation for student debt load is $4,200.The α is set to 0.05.The p-value for this hypothesis test would be ______.

A Type II error occurs when we ___________.

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20.In a sample of 200 graduates,30 students have a GPA of 3.00 or below.In testing the university's belief,the appropriate hypotheses are __________.

When conducting a hypothesis test concerning the population proportion,the value of the test statistic is calculated as ____________.

A professional sports organization is going to implement a test for steroids.The test gives a positive reaction in 94% of the people who have taken the steroid.However,it erroneously gives a positive reaction in 4% of the people who have not taken the steroid.What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids."

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose,on average,more than 10 pounds.A consumer activist decides to test the authenticity of the claim.She follows the progress of 18 women who recently joined the weight-reduction program.She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds.The test statistic for this hypothesis would be _______.

The national average for an eighth-grade reading comprehension test is 73.A school district claims that its eighth-graders outperform the national average.In testing the school district's claim,how does one define the population parameter of interest?

A schoolteacher is worried that the concentration of dangerous,cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L.The value of the test statistic is ___________.

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose,on average,more than 10 pounds.A consumer activist decides to test the authenticity of the claim.She follows the progress of 18 women who recently joined the weight-reduction program.She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds.At the 5% significance level,the critical value would be ______.

The percentage of complete passes is an important measure for a quarterback in the NFL.A particular quarterback has a career completion percentage of 55%.The quarterback got a new coach and then played a few games where he completed 48 of 100 passes. a.Specify the null and alternative hypotheses to determine whether the proportion of completed passes has decreased with the new coach. b.Calculate the value of the test statistic and the p-value. c.At the 5% significance level,can you conclude that the quarterback's completion percentage has decreased?

Which of the following types of tests may be performed?

A fast-food franchise is considering building a restaurant at a busy intersection.A financial advisor determines that the site is acceptable only if,on average,more than 300 automobiles pass the location per hour.The advisor tests the following hypotheses: H_o: μ ≤ 300. H_A: μ > 300. The consequences of committing a Type II error would be that__________________________.

Billy wants to test whether the average speed of his favorite pitcher's fastball differs from the league average of 92 miles per hour.He takes a sample of 36 of the pitcher's fastballs and computes a sample mean of 94 miles per hour.Assume that the standard deviation of the population is 4 miles per hour. a.Specify the null and alternative hypotheses to test Billy's claim. b.Calculate the value of the test statistic and the p-value. c.At the 5% significance level,can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average? d.At the 1% significance level,can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average?

If the chosen significance level is α = 0.05,then ____________________________________________.

For a given sample size n,_______________________________________________________________.

Massachusetts Institute of Technology grants pirate certificates to those students who successfully complete courses in archery,fencing,sailing,and pistol shooting ("MIT Awards Pirate Certificates to Undergraduates," Boston Globe,March 3,2012).Sheila claims that those students who go on to earn pirate certificates are able to hit a higher proportion of bull's-eyes during the archery final exam than the course average of 0.15.Specify the null and alternative hypotheses to test her claim.

A schoolteacher is worried that the concentration of dangerous,cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L.At a 5% significance level,the critical value(s)is(are)_______.

A philanthropic organization helped a town in Africa dig several wells to gain access to clean water.Before the wells were in place,an average of 120 infants contracted typhoid each month.After the wells were installed,the philanthropic organization surveyed for nine months and found an average of 90 infants contracted typhoid per month.Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed. a.Specify the null and alternative hypotheses to determine whether the average number of infants that contract typhoid has decreased because the wells were put in place. b.Calculate the value of the test statistic and the p-value. c.At the 5% significance level,can you conclude that the number of babies falling ill due to typhoid has decreased? Explain.