Exam 9: Hypothesis Testing

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). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire this year, 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. Which of the following should be used to develop the null and alternative hypotheses to test this 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. The value of the test statistic is ________.

For a given sample size n, ________.

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. At a 5% significance level, the decision is to ________.

A city is considering widening a busy intersection in town. Last year, the city reported 16,000 cars passed through the intersection per day. The city conducted a survey for 49 days this year and found an average of 17,000 cars passed through the intersection, with a standard deviation of 5,000. A) Specify the null and alternative hypotheses to determine whether the intersection has seen an increase in traffic. B) Calculate the value of the test statistic and the p-value. C) The city is going to widen the intersection if it believes traffic has increased. At the 5% significance level, can you conclude that the intersection has seen an increase in traffic? Should the city widen the intersection?

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

Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. Which of the following hypothesis tests should be performed?

A(n) ________ error is committed when we reject the null hypothesis when the null hypothesis is true.

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 ________.

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. At a 5% significance level, the decision is to ________.

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 ________.

Students who graduated from college in last year with student loans owed an average of $25,250 (The New York Times, November 2). An economist wants to determine if the average debt has increased since last year. She takes a sample of 40 recent graduates and finds that their average debt was $28,275. Assume that the population standard deviation is $7,250. A) Specify the competing hypotheses to determine whether the average undergraduate debt has increased since last year. B) Calculate the value of the test statistic and the p-value. C) At the 5% significance level, can you conclude that the average undergraduate debt has increased? Explain.

Excel's function ________ returns the p-value for a right-tailed test of the population mean, when the raw data is available and is known.

When conducting a hypothesis test, which of the following decisions represents an error?

A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, H₀: μ ≥ 6 and H_A: μ < 6, μ stand for ________.

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?

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 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. The test statistic for this hypothesis would be ________.

An engineer wants to know if the average amount of energy used in his factory per day has changed since last year. The factory used an average of 2,000 megawatt hours (mwh) per day prior to last year. Since last year, 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.

Which of the following are two-tailed tests?