Exam 9: Hypothesis Testing

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.The value of the test statistic and its associated p-value are ________________________.

In general,the null and alternative hypotheses are __________.

A Massachusetts state police officer measured the speed of 100 motorists on the Massachusetts Turnpike and found that 70 exceeded the posted speed limit by more than 10 miles per hour.The police officer claims that more than 60% of motorists drive at least 10 miles per hour more than the posted speed on the turnpike. a.Specify the null and alternative hypotheses to test the officer's claim. b.Calculate the value of the test statistic. c.At the 5% significance level,what is(are)the critical value(s)to test the officer's claim? d.At the 5% significance level,does the evidence support the officer's 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.To test whether the average level of radon gas is greater than the safe level,the appropriate hypotheses are _____________________.

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 I error would be that____________________________.

When we reject the null hypothesis when it is actually false,we have committed _________.

The critical value approach specifies a region of values,also called the ________ region.

To test if the mean returns on a major index have changed from the historic monthly average of 1.2%,a sample of 36 recent monthly returns is used to calculate the value of the relevant t_df test statistic.At the 5% level of significance,we reject the null hypothesis if this value is ____________.

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.The value of the test statistic is ____________.

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.Which of the following can be used to determine whether the schedule adjustment reduced the average lateness time of 12 minutes?

A company has developed a new diet that it claims will lower one's weight by more than 10 pounds.Health officials decide to conduct a test to validate this claim.The consumers should be _____________________________________.

A doctor thinks he has found a miraculous cure for rheumatoid arthritis.He thinks it will cure more than 50% of all cases within a year of first taking the drug.To test his drug,he runs a clinical trial on 400 patients with rheumatoid arthritis.He finds that 208 of the patients are symptomfree within a year. a.Specify the null and alternative hypotheses to determine whether the proportion of patients that are cured by the drug exceeds 50%. b.Calculate the value of the test statistic,and find the critical value at a 5% significance level. c.At the 5% significance level,can you conclude that the percentage of patients who are cured by the drug exceeds 50%?

The _______ value approach specifies a region of values such that if the value of the test statistic falls into this region,then we reject the null hypothesis.

Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States,with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune,February 26,2011).But Keurig's patent on K-cups,the plastic pods used to brew the coffee,is expected to expire in 2012,allowing other companies to better compete.Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters.After tweaking its recipe,the competitor conducts a test with 144 tasters,of which 72 prefer its blend.The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast.At the 1% significance level,does the evidence support the claim?

A real estate investor thinks the real estate market has bottomed out.One of the variables he examined to arrive at this conclusion was the proportion of houses sold at or above the asking price.In 2010,the proportion of houses sold at or above the asking price was 14%.The real estate investor takes a random sample of 40 recently sold houses and finds that nine of them are selling at or above the asking price. a.Specify the population parameter to be tested. b.Specify the null and alternative hypotheses to determine whether the proportion of houses sold at or above the asking price has increased. c.Calculate the value of the test statistic and the p-value. d.At the 10% significance level,can you conclude that the proportion of houses sold at or above the asking price has increased?

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 confidence interval for this hypothesis test would be __________________.

We define the allowed probability of making a Type I error as α,and we refer to 100α% as the ____________.

A local courier service advertises that its average delivery time is less than 6 hours for local deliveries.When testing the two hypotheses,H_o:μ ≥ 6 and H_A:μ < 6,μ stand for _____________.

A two-tailed hypothesis test of the population mean or population proportion has ________.

An engineer wants to know if the average amount of energy used in his factory per day has changed since 2005.The factory used an average of 2,000 megawatt hours (mwh)per day prior to 2005.Since 2005,the engineer surveyed 400 days and found the average energy use was 2,040 mwh per day.Assume that the population standard deviation is 425 mwh per day. a.Specify the null and alternative hypotheses to determine whether the factory's energy use has changed. b.Calculate the value of the test statistic and the p-value. c.At the 5% significance level,can you conclude that the energy usage has changed? Explain.